Datasets:

internlm
/

Lean-Github

url stringclasses 147 values	commit stringclasses 147 values	file_path stringlengths 7 101	full_name stringlengths 1 94	start stringlengths 6 10	end stringlengths 6 11	tactic stringlengths 1 11.2k	state_before stringlengths 3 2.09M	state_after stringlengths 6 2.09M
https://github.com/kevinsullivan/cs2120f23.git	c2da7c4a6be769c6fca375a54e8c1fa31ba2854b	Instructor/Lectures/grad/vector_spaces.lean	rot_add_assoc	[134, 1]	[144, 4]	intros a b c	⊢ ∀ (a b c : Rotation), a + b + c = a + (b + c)	a b c : Rotation ⊢ a + b + c = a + (b + c)
https://github.com/kevinsullivan/cs2120f23.git	c2da7c4a6be769c6fca375a54e8c1fa31ba2854b	Instructor/Lectures/grad/vector_spaces.lean	rot_add_assoc	[134, 1]	[144, 4]	cases a	a b c : Rotation ⊢ a + b + c = a + (b + c)	case r0 b c : Rotation ⊢ r0 + b + c = r0 + (b + c) case r120 b c : Rotation ⊢ r120 + b + c = r120 + (b + c) case r240 b c : Rotation ⊢ r240 + b + c = r240 + (b + c)
https://github.com/kevinsullivan/cs2120f23.git	c2da7c4a6be769c6fca375a54e8c1fa31ba2854b	Instructor/Lectures/grad/vector_spaces.lean	rot_add_assoc	[134, 1]	[144, 4]	repeat { cases b repeat { cases c repeat { rfl } } }	case r0 b c : Rotation ⊢ r0 + b + c = r0 + (b + c) case r120 b c : Rotation ⊢ r120 + b + c = r120 + (b + c) case r240 b c : Rotation ⊢ r240 + b + c = r240 + (b + c)	no goals
https://github.com/kevinsullivan/cs2120f23.git	c2da7c4a6be769c6fca375a54e8c1fa31ba2854b	Instructor/Lectures/grad/vector_spaces.lean	rot_add_assoc	[134, 1]	[144, 4]	cases b	case r240 b c : Rotation ⊢ r240 + b + c = r240 + (b + c)	case r240.r0 c : Rotation ⊢ r240 + r0 + c = r240 + (r0 + c) case r240.r120 c : Rotation ⊢ r240 + r120 + c = r240 + (r120 + c) case r240.r240 c : Rotation ⊢ r240 + r240 + c = r240 + (r240 + c)
https://github.com/kevinsullivan/cs2120f23.git	c2da7c4a6be769c6fca375a54e8c1fa31ba2854b	Instructor/Lectures/grad/vector_spaces.lean	rot_add_assoc	[134, 1]	[144, 4]	repeat { cases c repeat { rfl } }	case r240.r0 c : Rotation ⊢ r240 + r0 + c = r240 + (r0 + c) case r240.r120 c : Rotation ⊢ r240 + r120 + c = r240 + (r120 + c) case r240.r240 c : Rotation ⊢ r240 + r240 + c = r240 + (r240 + c)	no goals
https://github.com/kevinsullivan/cs2120f23.git	c2da7c4a6be769c6fca375a54e8c1fa31ba2854b	Instructor/Lectures/grad/vector_spaces.lean	rot_add_assoc	[134, 1]	[144, 4]	cases c	case r240.r240 c : Rotation ⊢ r240 + r240 + c = r240 + (r240 + c)	case r240.r240.r0 ⊢ r240 + r240 + r0 = r240 + (r240 + r0) case r240.r240.r120 ⊢ r240 + r240 + r120 = r240 + (r240 + r120) case r240.r240.r240 ⊢ r240 + r240 + r240 = r240 + (r240 + r240)
https://github.com/kevinsullivan/cs2120f23.git	c2da7c4a6be769c6fca375a54e8c1fa31ba2854b	Instructor/Lectures/grad/vector_spaces.lean	rot_add_assoc	[134, 1]	[144, 4]	repeat { rfl }	case r240.r240.r0 ⊢ r240 + r240 + r0 = r240 + (r240 + r0) case r240.r240.r120 ⊢ r240 + r240 + r120 = r240 + (r240 + r120) case r240.r240.r240 ⊢ r240 + r240 + r240 = r240 + (r240 + r240)	no goals
https://github.com/kevinsullivan/cs2120f23.git	c2da7c4a6be769c6fca375a54e8c1fa31ba2854b	Instructor/Lectures/grad/vector_spaces.lean	rot_add_assoc	[134, 1]	[144, 4]	rfl	case r240.r240.r240 ⊢ r240 + r240 + r240 = r240 + (r240 + r240)	no goals
https://github.com/kevinsullivan/cs2120f23.git	c2da7c4a6be769c6fca375a54e8c1fa31ba2854b	Instructor/Lectures/grad/vector_spaces.lean	rot_zero_add	[157, 1]	[161, 17]	intro a	⊢ ∀ (a : Rotation), 0 + a = a	a : Rotation ⊢ 0 + a = a
https://github.com/kevinsullivan/cs2120f23.git	c2da7c4a6be769c6fca375a54e8c1fa31ba2854b	Instructor/Lectures/grad/vector_spaces.lean	rot_zero_add	[157, 1]	[161, 17]	cases a	a : Rotation ⊢ 0 + a = a	case r0 ⊢ 0 + r0 = r0 case r120 ⊢ 0 + r120 = r120 case r240 ⊢ 0 + r240 = r240
https://github.com/kevinsullivan/cs2120f23.git	c2da7c4a6be769c6fca375a54e8c1fa31ba2854b	Instructor/Lectures/grad/vector_spaces.lean	rot_zero_add	[157, 1]	[161, 17]	repeat { rfl }	case r0 ⊢ 0 + r0 = r0 case r120 ⊢ 0 + r120 = r120 case r240 ⊢ 0 + r240 = r240	no goals
https://github.com/kevinsullivan/cs2120f23.git	c2da7c4a6be769c6fca375a54e8c1fa31ba2854b	Instructor/Lectures/grad/vector_spaces.lean	rot_zero_add	[157, 1]	[161, 17]	rfl	case r240 ⊢ 0 + r240 = r240	no goals
https://github.com/kevinsullivan/cs2120f23.git	c2da7c4a6be769c6fca375a54e8c1fa31ba2854b	Instructor/Lectures/grad/vector_spaces.lean	rot_add_zero	[163, 1]	[167, 17]	intro a	⊢ ∀ (a : Rotation), a + 0 = a	a : Rotation ⊢ a + 0 = a
https://github.com/kevinsullivan/cs2120f23.git	c2da7c4a6be769c6fca375a54e8c1fa31ba2854b	Instructor/Lectures/grad/vector_spaces.lean	rot_add_zero	[163, 1]	[167, 17]	cases a	a : Rotation ⊢ a + 0 = a	case r0 ⊢ r0 + 0 = r0 case r120 ⊢ r120 + 0 = r120 case r240 ⊢ r240 + 0 = r240
https://github.com/kevinsullivan/cs2120f23.git	c2da7c4a6be769c6fca375a54e8c1fa31ba2854b	Instructor/Lectures/grad/vector_spaces.lean	rot_add_zero	[163, 1]	[167, 17]	repeat { rfl }	case r0 ⊢ r0 + 0 = r0 case r120 ⊢ r120 + 0 = r120 case r240 ⊢ r240 + 0 = r240	no goals
https://github.com/kevinsullivan/cs2120f23.git	c2da7c4a6be769c6fca375a54e8c1fa31ba2854b	Instructor/Lectures/grad/vector_spaces.lean	rot_add_zero	[163, 1]	[167, 17]	rfl	case r240 ⊢ r240 + 0 = r240	no goals
https://github.com/kevinsullivan/cs2120f23.git	c2da7c4a6be769c6fca375a54e8c1fa31ba2854b	Instructor/Lectures/grad/vector_spaces.lean	rot_zero_vadd	[219, 1]	[223, 17]	intro p	⊢ ∀ (p : State), 0 +ᵥ p = p	p : State ⊢ 0 +ᵥ p = p
https://github.com/kevinsullivan/cs2120f23.git	c2da7c4a6be769c6fca375a54e8c1fa31ba2854b	Instructor/Lectures/grad/vector_spaces.lean	rot_zero_vadd	[219, 1]	[223, 17]	cases p	p : State ⊢ 0 +ᵥ p = p	case heading h✝ : K unit✝ : ℕ ⊢ 0 +ᵥ heading h✝ unit✝ = heading h✝ unit✝
https://github.com/kevinsullivan/cs2120f23.git	c2da7c4a6be769c6fca375a54e8c1fa31ba2854b	Instructor/Lectures/grad/vector_spaces.lean	rot_zero_vadd	[219, 1]	[223, 17]	repeat { rfl }	case heading h✝ : K unit✝ : ℕ ⊢ 0 +ᵥ heading h✝ unit✝ = heading h✝ unit✝	no goals
https://github.com/kevinsullivan/cs2120f23.git	c2da7c4a6be769c6fca375a54e8c1fa31ba2854b	Instructor/Lectures/grad/vector_spaces.lean	rot_zero_vadd	[219, 1]	[223, 17]	rfl	case heading h✝ : K unit✝ : ℕ ⊢ 0 +ᵥ heading h✝ unit✝ = heading h✝ unit✝	no goals
https://github.com/kevinsullivan/cs2120f23.git	c2da7c4a6be769c6fca375a54e8c1fa31ba2854b	Instructor/Lectures/grad/vector_spaces.lean	rot_add_vadd	[225, 1]	[235, 4]	intros g₁ g₂ p	⊢ ∀ (g₁ g₂ : Rotation) (p : State), g₁ + g₂ +ᵥ p = g₁ +ᵥ (g₂ +ᵥ p)	g₁ g₂ : Rotation p : State ⊢ g₁ + g₂ +ᵥ p = g₁ +ᵥ (g₂ +ᵥ p)
https://github.com/kevinsullivan/cs2120f23.git	c2da7c4a6be769c6fca375a54e8c1fa31ba2854b	Instructor/Lectures/grad/vector_spaces.lean	rot_add_vadd	[225, 1]	[235, 4]	cases g₁	g₁ g₂ : Rotation p : State ⊢ g₁ + g₂ +ᵥ p = g₁ +ᵥ (g₂ +ᵥ p)	case r0 g₂ : Rotation p : State ⊢ r0 + g₂ +ᵥ p = r0 +ᵥ (g₂ +ᵥ p) case r120 g₂ : Rotation p : State ⊢ r120 + g₂ +ᵥ p = r120 +ᵥ (g₂ +ᵥ p) case r240 g₂ : Rotation p : State ⊢ r240 + g₂ +ᵥ p = r240 +ᵥ (g₂ +ᵥ p)
https://github.com/kevinsullivan/cs2120f23.git	c2da7c4a6be769c6fca375a54e8c1fa31ba2854b	Instructor/Lectures/grad/vector_spaces.lean	rot_add_vadd	[225, 1]	[235, 4]	repeat { cases g₂ repeat { cases p repeat rfl } }	case r0 g₂ : Rotation p : State ⊢ r0 + g₂ +ᵥ p = r0 +ᵥ (g₂ +ᵥ p) case r120 g₂ : Rotation p : State ⊢ r120 + g₂ +ᵥ p = r120 +ᵥ (g₂ +ᵥ p) case r240 g₂ : Rotation p : State ⊢ r240 + g₂ +ᵥ p = r240 +ᵥ (g₂ +ᵥ p)	case r120 g₂ : Rotation p : State ⊢ r120 + g₂ +ᵥ p = r120 +ᵥ (g₂ +ᵥ p) case r240 g₂ : Rotation p : State ⊢ r240 + g₂ +ᵥ p = r240 +ᵥ (g₂ +ᵥ p)
https://github.com/kevinsullivan/cs2120f23.git	c2da7c4a6be769c6fca375a54e8c1fa31ba2854b	Instructor/Lectures/grad/vector_spaces.lean	rot_add_vadd	[225, 1]	[235, 4]	cases g₂	case r120 g₂ : Rotation p : State ⊢ r120 + g₂ +ᵥ p = r120 +ᵥ (g₂ +ᵥ p)	case r120.r0 p : State ⊢ r120 + r0 +ᵥ p = r120 +ᵥ (r0 +ᵥ p) case r120.r120 p : State ⊢ r120 + r120 +ᵥ p = r120 +ᵥ (r120 +ᵥ p) case r120.r240 p : State ⊢ r120 + r240 +ᵥ p = r120 +ᵥ (r240 +ᵥ p)
https://github.com/kevinsullivan/cs2120f23.git	c2da7c4a6be769c6fca375a54e8c1fa31ba2854b	Instructor/Lectures/grad/vector_spaces.lean	rot_add_vadd	[225, 1]	[235, 4]	repeat { cases p repeat rfl }	case r120.r0 p : State ⊢ r120 + r0 +ᵥ p = r120 +ᵥ (r0 +ᵥ p) case r120.r120 p : State ⊢ r120 + r120 +ᵥ p = r120 +ᵥ (r120 +ᵥ p) case r120.r240 p : State ⊢ r120 + r240 +ᵥ p = r120 +ᵥ (r240 +ᵥ p)	case r120.r240 p : State ⊢ r120 + r240 +ᵥ p = r120 +ᵥ (r240 +ᵥ p)
https://github.com/kevinsullivan/cs2120f23.git	c2da7c4a6be769c6fca375a54e8c1fa31ba2854b	Instructor/Lectures/grad/vector_spaces.lean	rot_add_vadd	[225, 1]	[235, 4]	cases p	case r120.r240 p : State ⊢ r120 + r240 +ᵥ p = r120 +ᵥ (r240 +ᵥ p)	case r120.r240.heading h✝ : K unit✝ : ℕ ⊢ r120 + r240 +ᵥ heading h✝ unit✝ = r120 +ᵥ (r240 +ᵥ heading h✝ unit✝)
https://github.com/kevinsullivan/cs2120f23.git	c2da7c4a6be769c6fca375a54e8c1fa31ba2854b	Instructor/Lectures/grad/vector_spaces.lean	rot_add_vadd	[225, 1]	[235, 4]	repeat rfl	case r120.r120.heading h✝ : K unit✝ : ℕ ⊢ r120 + r120 +ᵥ heading h✝ unit✝ = r120 +ᵥ (r120 +ᵥ heading h✝ unit✝)	no goals
https://github.com/kevinsullivan/cs2120f23.git	c2da7c4a6be769c6fca375a54e8c1fa31ba2854b	Instructor/Lectures/grad/vector_spaces.lean	rot_add_vadd	[225, 1]	[235, 4]	rfl	case r120.r120.heading h✝ : K unit✝ : ℕ ⊢ r120 + r120 +ᵥ heading h✝ unit✝ = r120 +ᵥ (r120 +ᵥ heading h✝ unit✝)	no goals
https://github.com/kevinsullivan/cs2120f23.git	c2da7c4a6be769c6fca375a54e8c1fa31ba2854b	Instructor/Lectures/grad/vector_spaces.lean	rot_add_neg_left	[349, 1]	[353, 17]	intro a	⊢ ∀ (a : Rotation), -a + a = 0	a : Rotation ⊢ -a + a = 0
https://github.com/kevinsullivan/cs2120f23.git	c2da7c4a6be769c6fca375a54e8c1fa31ba2854b	Instructor/Lectures/grad/vector_spaces.lean	rot_add_neg_left	[349, 1]	[353, 17]	cases a	a : Rotation ⊢ -a + a = 0	case r0 ⊢ -r0 + r0 = 0 case r120 ⊢ -r120 + r120 = 0 case r240 ⊢ -r240 + r240 = 0
https://github.com/kevinsullivan/cs2120f23.git	c2da7c4a6be769c6fca375a54e8c1fa31ba2854b	Instructor/Lectures/grad/vector_spaces.lean	rot_add_neg_left	[349, 1]	[353, 17]	repeat { rfl }	case r0 ⊢ -r0 + r0 = 0 case r120 ⊢ -r120 + r120 = 0 case r240 ⊢ -r240 + r240 = 0	no goals
https://github.com/kevinsullivan/cs2120f23.git	c2da7c4a6be769c6fca375a54e8c1fa31ba2854b	Instructor/Lectures/grad/vector_spaces.lean	rot_add_neg_left	[349, 1]	[353, 17]	rfl	case r240 ⊢ -r240 + r240 = 0	no goals
https://github.com/kevinsullivan/cs2120f23.git	c2da7c4a6be769c6fca375a54e8c1fa31ba2854b	Instructor/Lectures/grad/vector_spaces.lean	rot_state_vsub_vadd'	[405, 1]	[412, 4]	intro p1 p2	⊢ ∀ (p1 p2 : State), p1 -ᵥ p2 +ᵥ p2 = p1	p1 p2 : State ⊢ p1 -ᵥ p2 +ᵥ p2 = p1
https://github.com/kevinsullivan/cs2120f23.git	c2da7c4a6be769c6fca375a54e8c1fa31ba2854b	Instructor/Lectures/grad/vector_spaces.lean	rot_state_vsub_vadd'	[405, 1]	[412, 4]	cases p1	p1 p2 : State ⊢ p1 -ᵥ p2 +ᵥ p2 = p1	case heading p2 : State h✝ : K unit✝ : ℕ ⊢ heading h✝ unit✝ -ᵥ p2 +ᵥ p2 = heading h✝ unit✝
https://github.com/kevinsullivan/cs2120f23.git	c2da7c4a6be769c6fca375a54e8c1fa31ba2854b	Instructor/Lectures/grad/vector_spaces.lean	rot_state_vsub_vadd'	[405, 1]	[412, 4]	cases p2	case heading p2 : State h✝ : K unit✝ : ℕ ⊢ heading h✝ unit✝ -ᵥ p2 +ᵥ p2 = heading h✝ unit✝	case heading.heading h✝¹ : K unit✝¹ : ℕ h✝ : K unit✝ : ℕ ⊢ heading h✝¹ unit✝¹ -ᵥ heading h✝ unit✝ +ᵥ heading h✝ unit✝ = heading h✝¹ unit✝¹
https://github.com/kevinsullivan/cs2120f23.git	c2da7c4a6be769c6fca375a54e8c1fa31ba2854b	Instructor/Lectures/grad/vector_spaces.lean	rot_state_vadd_vsub'	[414, 1]	[421, 4]	intros g p	⊢ ∀ (g : Rotation) (p : State), g +ᵥ p -ᵥ p = g	g : Rotation p : State ⊢ g +ᵥ p -ᵥ p = g
https://github.com/kevinsullivan/cs2120f23.git	c2da7c4a6be769c6fca375a54e8c1fa31ba2854b	Instructor/Lectures/grad/vector_spaces.lean	rot_state_vadd_vsub'	[414, 1]	[421, 4]	cases g	g : Rotation p : State ⊢ g +ᵥ p -ᵥ p = g	case r0 p : State ⊢ r0 +ᵥ p -ᵥ p = r0 case r120 p : State ⊢ r120 +ᵥ p -ᵥ p = r120 case r240 p : State ⊢ r240 +ᵥ p -ᵥ p = r240
https://github.com/kevinsullivan/cs2120f23.git	c2da7c4a6be769c6fca375a54e8c1fa31ba2854b	Instructor/Lectures/grad/vector_spaces.lean	rot_state_vadd_vsub'	[414, 1]	[421, 4]	cases p	case r0 p : State ⊢ r0 +ᵥ p -ᵥ p = r0	case r0.heading h✝ : K unit✝ : ℕ ⊢ r0 +ᵥ heading h✝ unit✝ -ᵥ heading h✝ unit✝ = r0
https://github.com/kevinsullivan/cs2120f23.git	c2da7c4a6be769c6fca375a54e8c1fa31ba2854b	Instructor/Lectures/grad/sets_relations.lean	eq_nat_is_refl	[68, 1]	[71, 12]	unfold Reflexive	⊢ Reflexive Eq	⊢ ∀ (x : ℕ), x = x
https://github.com/kevinsullivan/cs2120f23.git	c2da7c4a6be769c6fca375a54e8c1fa31ba2854b	Instructor/Lectures/grad/sets_relations.lean	eq_nat_is_refl	[68, 1]	[71, 12]	intro x	⊢ ∀ (x : ℕ), x = x	x : ℕ ⊢ x = x
https://github.com/kevinsullivan/cs2120f23.git	c2da7c4a6be769c6fca375a54e8c1fa31ba2854b	Instructor/Lectures/grad/sets_relations.lean	eq_nat_is_refl	[68, 1]	[71, 12]	exact rfl	x : ℕ ⊢ x = x	no goals
https://github.com/kevinsullivan/cs2120f23.git	c2da7c4a6be769c6fca375a54e8c1fa31ba2854b	Instructor/Lectures/grad/sets_relations.lean	eq_nat_is_symm	[73, 1]	[77, 11]	unfold Symmetric	⊢ Symmetric Eq	⊢ ∀ ⦃x y : ℕ⦄, x = y → y = x
https://github.com/kevinsullivan/cs2120f23.git	c2da7c4a6be769c6fca375a54e8c1fa31ba2854b	Instructor/Lectures/grad/sets_relations.lean	eq_nat_is_symm	[73, 1]	[77, 11]	intro x y	⊢ ∀ ⦃x y : ℕ⦄, x = y → y = x	x y : ℕ ⊢ x = y → y = x
https://github.com/kevinsullivan/cs2120f23.git	c2da7c4a6be769c6fca375a54e8c1fa31ba2854b	Instructor/Lectures/grad/sets_relations.lean	eq_nat_is_symm	[73, 1]	[77, 11]	intro hxy	x y : ℕ ⊢ x = y → y = x	x y : ℕ hxy : x = y ⊢ y = x
https://github.com/kevinsullivan/cs2120f23.git	c2da7c4a6be769c6fca375a54e8c1fa31ba2854b	Instructor/Lectures/grad/sets_relations.lean	eq_nat_is_symm	[73, 1]	[77, 11]	rw [hxy]	x y : ℕ hxy : x = y ⊢ y = x	no goals
https://github.com/kevinsullivan/cs2120f23.git	c2da7c4a6be769c6fca375a54e8c1fa31ba2854b	Instructor/Lectures/grad/sets_relations.lean	eq_nat_is_trans	[82, 1]	[87, 9]	unfold Transitive	⊢ Transitive Eq	⊢ ∀ ⦃x y z : ℕ⦄, x = y → y = z → x = z
https://github.com/kevinsullivan/cs2120f23.git	c2da7c4a6be769c6fca375a54e8c1fa31ba2854b	Instructor/Lectures/grad/sets_relations.lean	eq_nat_is_trans	[82, 1]	[87, 9]	intros x y z	⊢ ∀ ⦃x y z : ℕ⦄, x = y → y = z → x = z	x y z : ℕ ⊢ x = y → y = z → x = z
https://github.com/kevinsullivan/cs2120f23.git	c2da7c4a6be769c6fca375a54e8c1fa31ba2854b	Instructor/Lectures/grad/sets_relations.lean	eq_nat_is_trans	[82, 1]	[87, 9]	intros hxy hyz	x y z : ℕ ⊢ x = y → y = z → x = z	x y z : ℕ hxy : x = y hyz : y = z ⊢ x = z
https://github.com/kevinsullivan/cs2120f23.git	c2da7c4a6be769c6fca375a54e8c1fa31ba2854b	Instructor/Lectures/grad/sets_relations.lean	eq_nat_is_trans	[82, 1]	[87, 9]	rw [hxy]	x y z : ℕ hxy : x = y hyz : y = z ⊢ x = z	x y z : ℕ hxy : x = y hyz : y = z ⊢ y = z
https://github.com/kevinsullivan/cs2120f23.git	c2da7c4a6be769c6fca375a54e8c1fa31ba2854b	Instructor/Lectures/grad/sets_relations.lean	eq_nat_is_trans	[82, 1]	[87, 9]	rw [hyz]	x y z : ℕ hxy : x = y hyz : y = z ⊢ y = z	no goals
https://github.com/kevinsullivan/cs2120f23.git	c2da7c4a6be769c6fca375a54e8c1fa31ba2854b	Instructor/Lectures/grad/sets_relations.lean	cong_mod_n_equiv'	[99, 1]	[102, 31]	intro n	⊢ ∀ (n : ℕ), Equivalence (cong_mod_n n)	n : ℕ ⊢ Equivalence (cong_mod_n n)
https://github.com/kevinsullivan/cs2120f23.git	c2da7c4a6be769c6fca375a54e8c1fa31ba2854b	Instructor/Lectures/grad/sets_relations.lean	cong_mod_n_rfl	[106, 1]	[111, 12]	intro n	⊢ ∀ (n : ℕ), Reflexive (cong_mod_n n)	n : ℕ ⊢ Reflexive (cong_mod_n n)
https://github.com/kevinsullivan/cs2120f23.git	c2da7c4a6be769c6fca375a54e8c1fa31ba2854b	Instructor/Lectures/grad/sets_relations.lean	cong_mod_n_rfl	[106, 1]	[111, 12]	unfold cong_mod_n	n : ℕ ⊢ Reflexive (cong_mod_n n)	n : ℕ ⊢ Reflexive fun a b => a % n = b % n
https://github.com/kevinsullivan/cs2120f23.git	c2da7c4a6be769c6fca375a54e8c1fa31ba2854b	Instructor/Lectures/grad/sets_relations.lean	cong_mod_n_rfl	[106, 1]	[111, 12]	unfold Reflexive	n : ℕ ⊢ Reflexive fun a b => a % n = b % n	n : ℕ ⊢ ∀ (x : ℕ), (fun a b => a % n = b % n) x x
https://github.com/kevinsullivan/cs2120f23.git	c2da7c4a6be769c6fca375a54e8c1fa31ba2854b	Instructor/Lectures/grad/sets_relations.lean	cong_mod_n_rfl	[106, 1]	[111, 12]	intro a	n : ℕ ⊢ ∀ (x : ℕ), (fun a b => a % n = b % n) x x	n a : ℕ ⊢ a % n = a % n
https://github.com/kevinsullivan/cs2120f23.git	c2da7c4a6be769c6fca375a54e8c1fa31ba2854b	Instructor/Lectures/grad/sets_relations.lean	cong_mod_n_rfl	[106, 1]	[111, 12]	exact rfl	n a : ℕ ⊢ a % n = a % n	no goals
https://github.com/kevinsullivan/cs2120f23.git	c2da7c4a6be769c6fca375a54e8c1fa31ba2854b	Instructor/Lectures/grad/sets_relations.lean	cong_mod_n_symm	[113, 1]	[120, 11]	intro n	⊢ ∀ (n : ℕ), Symmetric (cong_mod_n n)	n : ℕ ⊢ Symmetric (cong_mod_n n)
https://github.com/kevinsullivan/cs2120f23.git	c2da7c4a6be769c6fca375a54e8c1fa31ba2854b	Instructor/Lectures/grad/sets_relations.lean	cong_mod_n_symm	[113, 1]	[120, 11]	unfold Symmetric	n : ℕ ⊢ Symmetric (cong_mod_n n)	n : ℕ ⊢ ∀ ⦃x y : ℕ⦄, cong_mod_n n x y → cong_mod_n n y x
https://github.com/kevinsullivan/cs2120f23.git	c2da7c4a6be769c6fca375a54e8c1fa31ba2854b	Instructor/Lectures/grad/sets_relations.lean	cong_mod_n_symm	[113, 1]	[120, 11]	intros x y	n : ℕ ⊢ ∀ ⦃x y : ℕ⦄, cong_mod_n n x y → cong_mod_n n y x	n x y : ℕ ⊢ cong_mod_n n x y → cong_mod_n n y x
https://github.com/kevinsullivan/cs2120f23.git	c2da7c4a6be769c6fca375a54e8c1fa31ba2854b	Instructor/Lectures/grad/sets_relations.lean	cong_mod_n_symm	[113, 1]	[120, 11]	intro hxy	n x y : ℕ ⊢ cong_mod_n n x y → cong_mod_n n y x	n x y : ℕ hxy : cong_mod_n n x y ⊢ cong_mod_n n y x
https://github.com/kevinsullivan/cs2120f23.git	c2da7c4a6be769c6fca375a54e8c1fa31ba2854b	Instructor/Lectures/grad/sets_relations.lean	cong_mod_n_symm	[113, 1]	[120, 11]	unfold cong_mod_n	n x y : ℕ hxy : cong_mod_n n x y ⊢ cong_mod_n n y x	n x y : ℕ hxy : cong_mod_n n x y ⊢ y % n = x % n
https://github.com/kevinsullivan/cs2120f23.git	c2da7c4a6be769c6fca375a54e8c1fa31ba2854b	Instructor/Lectures/grad/sets_relations.lean	cong_mod_n_symm	[113, 1]	[120, 11]	unfold cong_mod_n at hxy	n x y : ℕ hxy : cong_mod_n n x y ⊢ y % n = x % n	n x y : ℕ hxy : x % n = y % n ⊢ y % n = x % n
https://github.com/kevinsullivan/cs2120f23.git	c2da7c4a6be769c6fca375a54e8c1fa31ba2854b	Instructor/Lectures/grad/sets_relations.lean	cong_mod_n_symm	[113, 1]	[120, 11]	rw [hxy]	n x y : ℕ hxy : x % n = y % n ⊢ y % n = x % n	no goals
https://github.com/kevinsullivan/cs2120f23.git	c2da7c4a6be769c6fca375a54e8c1fa31ba2854b	Instructor/Lectures/grad/sets_relations.lean	cong_mod_trans	[122, 1]	[126, 16]	intro n a b c hab hbc	⊢ ∀ (n : ℕ), Transitive (cong_mod_n n)	n a b c : ℕ hab : cong_mod_n n a b hbc : cong_mod_n n b c ⊢ cong_mod_n n a c
https://github.com/kevinsullivan/cs2120f23.git	c2da7c4a6be769c6fca375a54e8c1fa31ba2854b	Instructor/Lectures/grad/sets_relations.lean	cong_mod_trans	[122, 1]	[126, 16]	unfold cong_mod_n	n a b c : ℕ hab : cong_mod_n n a b hbc : cong_mod_n n b c ⊢ cong_mod_n n a c	n a b c : ℕ hab : cong_mod_n n a b hbc : cong_mod_n n b c ⊢ a % n = c % n
https://github.com/kevinsullivan/cs2120f23.git	c2da7c4a6be769c6fca375a54e8c1fa31ba2854b	Instructor/Lectures/grad/sets_relations.lean	cong_mod_trans	[122, 1]	[126, 16]	unfold cong_mod_n at hab hbc	n a b c : ℕ hab : cong_mod_n n a b hbc : cong_mod_n n b c ⊢ a % n = c % n	n a b c : ℕ hab : a % n = b % n hbc : b % n = c % n ⊢ a % n = c % n
https://github.com/kevinsullivan/cs2120f23.git	c2da7c4a6be769c6fca375a54e8c1fa31ba2854b	Instructor/Lectures/grad/sets_relations.lean	cong_mod_trans	[122, 1]	[126, 16]	rw [hab, hbc]	n a b c : ℕ hab : a % n = b % n hbc : b % n = c % n ⊢ a % n = c % n	no goals
https://github.com/kevinsullivan/cs2120f23.git	c2da7c4a6be769c6fca375a54e8c1fa31ba2854b	Instructor/Lectures/grad/sets_relations.lean	cong_mod_n_equiv	[128, 1]	[135, 47]	intro n	⊢ ∀ (n : ℕ), Equivalence (cong_mod_n n)	n : ℕ ⊢ Equivalence (cong_mod_n n)
https://github.com/kevinsullivan/cs2120f23.git	c2da7c4a6be769c6fca375a54e8c1fa31ba2854b	Instructor/Lectures/grad/sets_relations.lean	cong_mod_n_equiv	[128, 1]	[135, 47]	unfold cong_mod_n	n : ℕ ⊢ Equivalence (cong_mod_n n)	n : ℕ ⊢ Equivalence fun a b => a % n = b % n
https://github.com/kevinsullivan/cs2120f23.git	c2da7c4a6be769c6fca375a54e8c1fa31ba2854b	Instructor/Lectures/grad/sets_relations.lean	cong_mod_n_equiv	[128, 1]	[135, 47]	exact Equivalence.mk (by intro x; rfl) (by intros x y h; rw [h]) (by intros x y z hxy hyz; rw [hxy, hyz])	n : ℕ ⊢ Equivalence fun a b => a % n = b % n	no goals
https://github.com/kevinsullivan/cs2120f23.git	c2da7c4a6be769c6fca375a54e8c1fa31ba2854b	Instructor/Lectures/grad/sets_relations.lean	cong_mod_n_equiv	[128, 1]	[135, 47]	intro x	n : ℕ ⊢ ∀ (x : ℕ), x % n = x % n	n x : ℕ ⊢ x % n = x % n
https://github.com/kevinsullivan/cs2120f23.git	c2da7c4a6be769c6fca375a54e8c1fa31ba2854b	Instructor/Lectures/grad/sets_relations.lean	cong_mod_n_equiv	[128, 1]	[135, 47]	rfl	n x : ℕ ⊢ x % n = x % n	no goals
https://github.com/kevinsullivan/cs2120f23.git	c2da7c4a6be769c6fca375a54e8c1fa31ba2854b	Instructor/Lectures/grad/sets_relations.lean	cong_mod_n_equiv	[128, 1]	[135, 47]	intros x y h	n : ℕ ⊢ ∀ {x y : ℕ}, x % n = y % n → y % n = x % n	n x y : ℕ h : x % n = y % n ⊢ y % n = x % n
https://github.com/kevinsullivan/cs2120f23.git	c2da7c4a6be769c6fca375a54e8c1fa31ba2854b	Instructor/Lectures/grad/sets_relations.lean	cong_mod_n_equiv	[128, 1]	[135, 47]	rw [h]	n x y : ℕ h : x % n = y % n ⊢ y % n = x % n	no goals
https://github.com/kevinsullivan/cs2120f23.git	c2da7c4a6be769c6fca375a54e8c1fa31ba2854b	Instructor/Lectures/grad/sets_relations.lean	cong_mod_n_equiv	[128, 1]	[135, 47]	intros x y z hxy hyz	n : ℕ ⊢ ∀ {x y z : ℕ}, x % n = y % n → y % n = z % n → x % n = z % n	n x y z : ℕ hxy : x % n = y % n hyz : y % n = z % n ⊢ x % n = z % n
https://github.com/kevinsullivan/cs2120f23.git	c2da7c4a6be769c6fca375a54e8c1fa31ba2854b	Instructor/Lectures/grad/sets_relations.lean	cong_mod_n_equiv	[128, 1]	[135, 47]	rw [hxy, hyz]	n x y z : ℕ hxy : x % n = y % n hyz : y % n = z % n ⊢ x % n = z % n	no goals
https://github.com/kevinsullivan/cs2120f23.git	c2da7c4a6be769c6fca375a54e8c1fa31ba2854b	Instructor/Lectures/grad/sets_relations.lean	succ_inj	[189, 1]	[193, 13]	unfold Injective	⊢ Injective fun n => n + 1	⊢ ∀ ⦃a₁ a₂ : ℕ⦄, (fun n => n + 1) a₁ = (fun n => n + 1) a₂ → a₁ = a₂
https://github.com/kevinsullivan/cs2120f23.git	c2da7c4a6be769c6fca375a54e8c1fa31ba2854b	Instructor/Lectures/grad/sets_relations.lean	succ_inj	[189, 1]	[193, 13]	intros a1 a2 h	⊢ ∀ ⦃a₁ a₂ : ℕ⦄, (fun n => n + 1) a₁ = (fun n => n + 1) a₂ → a₁ = a₂	a1 a2 : ℕ h : (fun n => n + 1) a1 = (fun n => n + 1) a2 ⊢ a1 = a2
https://github.com/kevinsullivan/cs2120f23.git	c2da7c4a6be769c6fca375a54e8c1fa31ba2854b	Instructor/Lectures/grad/sets_relations.lean	succ_inj	[189, 1]	[193, 13]	simp [Nat.add] at h	a1 a2 : ℕ h : (fun n => n + 1) a1 = (fun n => n + 1) a2 ⊢ a1 = a2	a1 a2 : ℕ h : a1 = a2 ⊢ a1 = a2
https://github.com/kevinsullivan/cs2120f23.git	c2da7c4a6be769c6fca375a54e8c1fa31ba2854b	Instructor/Lectures/grad/sets_relations.lean	succ_inj	[189, 1]	[193, 13]	assumption	a1 a2 : ℕ h : a1 = a2 ⊢ a1 = a2	no goals
https://github.com/kevinsullivan/cs2120f23.git	c2da7c4a6be769c6fca375a54e8c1fa31ba2854b	Instructor/Lectures/grad/sets_relations.lean	not_succ_surj	[196, 1]	[200, 27]	unfold Surjective	⊢ ¬Surjective fun n => n + 1	⊢ ¬∀ (b : ℕ), ∃ a, (fun n => n + 1) a = b
https://github.com/kevinsullivan/cs2120f23.git	c2da7c4a6be769c6fca375a54e8c1fa31ba2854b	Instructor/Lectures/grad/sets_relations.lean	not_succ_surj	[196, 1]	[200, 27]	intro h	⊢ ¬∀ (b : ℕ), ∃ a, (fun n => n + 1) a = b	h : ∀ (b : ℕ), ∃ a, (fun n => n + 1) a = b ⊢ False
https://github.com/kevinsullivan/cs2120f23.git	c2da7c4a6be769c6fca375a54e8c1fa31ba2854b	Instructor/Lectures/grad/sets_relations.lean	not_succ_surj	[196, 1]	[200, 27]	let contra := h 0	h : ∀ (b : ℕ), ∃ a, (fun n => n + 1) a = b ⊢ False	h : ∀ (b : ℕ), ∃ a, (fun n => n + 1) a = b contra : ∃ a, (fun n => n + 1) a = 0 := h 0 ⊢ False
https://github.com/kevinsullivan/cs2120f23.git	c2da7c4a6be769c6fca375a54e8c1fa31ba2854b	Instructor/Lectures/grad/sets_relations.lean	not_succ_surj	[196, 1]	[200, 27]	simp [Nat.add] at contra	h : ∀ (b : ℕ), ∃ a, (fun n => n + 1) a = b contra : ∃ a, (fun n => n + 1) a = 0 := h 0 ⊢ False	no goals
https://github.com/kevinsullivan/cs2120f23.git	c2da7c4a6be769c6fca375a54e8c1fa31ba2854b	Instructor/Lectures/grad/sets_relations.lean	inj_not	[204, 1]	[215, 25]	unfold Injective	⊢ Injective Bool.not	⊢ ∀ ⦃a₁ a₂ : Bool⦄, Bool.not a₁ = Bool.not a₂ → a₁ = a₂
https://github.com/kevinsullivan/cs2120f23.git	c2da7c4a6be769c6fca375a54e8c1fa31ba2854b	Instructor/Lectures/grad/sets_relations.lean	inj_not	[204, 1]	[215, 25]	intros a1 a2 h	⊢ ∀ ⦃a₁ a₂ : Bool⦄, Bool.not a₁ = Bool.not a₂ → a₁ = a₂	a1 a2 : Bool h : Bool.not a1 = Bool.not a2 ⊢ a1 = a2
https://github.com/kevinsullivan/cs2120f23.git	c2da7c4a6be769c6fca375a54e8c1fa31ba2854b	Instructor/Lectures/grad/sets_relations.lean	inj_not	[204, 1]	[215, 25]	cases a1 with \| true => cases a2 with \| true => rfl \| false => nomatch h \| false => cases a2 with \| true => nomatch h \| false => rfl	a1 a2 : Bool h : Bool.not a1 = Bool.not a2 ⊢ a1 = a2	no goals
https://github.com/kevinsullivan/cs2120f23.git	c2da7c4a6be769c6fca375a54e8c1fa31ba2854b	Instructor/Lectures/grad/sets_relations.lean	inj_not	[204, 1]	[215, 25]	cases a2 with \| true => rfl \| false => nomatch h	case true a2 : Bool h : Bool.not true = Bool.not a2 ⊢ true = a2	no goals
https://github.com/kevinsullivan/cs2120f23.git	c2da7c4a6be769c6fca375a54e8c1fa31ba2854b	Instructor/Lectures/grad/sets_relations.lean	inj_not	[204, 1]	[215, 25]	rfl	case true.true h : Bool.not true = Bool.not true ⊢ true = true	no goals
https://github.com/kevinsullivan/cs2120f23.git	c2da7c4a6be769c6fca375a54e8c1fa31ba2854b	Instructor/Lectures/grad/sets_relations.lean	inj_not	[204, 1]	[215, 25]	nomatch h	case true.false h : Bool.not true = Bool.not false ⊢ true = false	no goals
https://github.com/kevinsullivan/cs2120f23.git	c2da7c4a6be769c6fca375a54e8c1fa31ba2854b	Instructor/Lectures/grad/sets_relations.lean	inj_not	[204, 1]	[215, 25]	cases a2 with \| true => nomatch h \| false => rfl	case false a2 : Bool h : Bool.not false = Bool.not a2 ⊢ false = a2	no goals
https://github.com/kevinsullivan/cs2120f23.git	c2da7c4a6be769c6fca375a54e8c1fa31ba2854b	Instructor/Lectures/grad/sets_relations.lean	inj_not	[204, 1]	[215, 25]	nomatch h	case false.true h : Bool.not false = Bool.not true ⊢ false = true	no goals
https://github.com/kevinsullivan/cs2120f23.git	c2da7c4a6be769c6fca375a54e8c1fa31ba2854b	Instructor/Lectures/grad/sets_relations.lean	inj_not	[204, 1]	[215, 25]	rfl	case false.false h : Bool.not false = Bool.not false ⊢ false = false	no goals
https://github.com/kevinsullivan/cs2120f23.git	c2da7c4a6be769c6fca375a54e8c1fa31ba2854b	Instructor/Lectures/grad/sets_relations.lean	surj_not	[217, 1]	[222, 33]	unfold Surjective	⊢ Surjective Bool.not	⊢ ∀ (b : Bool), ∃ a, Bool.not a = b
https://github.com/kevinsullivan/cs2120f23.git	c2da7c4a6be769c6fca375a54e8c1fa31ba2854b	Instructor/Lectures/grad/sets_relations.lean	surj_not	[217, 1]	[222, 33]	intro b	⊢ ∀ (b : Bool), ∃ a, Bool.not a = b	b : Bool ⊢ ∃ a, Bool.not a = b
https://github.com/kevinsullivan/cs2120f23.git	c2da7c4a6be769c6fca375a54e8c1fa31ba2854b	Instructor/Lectures/grad/sets_relations.lean	surj_not	[217, 1]	[222, 33]	cases b with \| true => exact ⟨ false, rfl ⟩ \| false => exact ⟨ true, rfl ⟩	b : Bool ⊢ ∃ a, Bool.not a = b	no goals
https://github.com/kevinsullivan/cs2120f23.git	c2da7c4a6be769c6fca375a54e8c1fa31ba2854b	Instructor/Lectures/grad/sets_relations.lean	surj_not	[217, 1]	[222, 33]	exact ⟨ false, rfl ⟩	case true ⊢ ∃ a, Bool.not a = true	no goals
https://github.com/kevinsullivan/cs2120f23.git	c2da7c4a6be769c6fca375a54e8c1fa31ba2854b	Instructor/Lectures/grad/sets_relations.lean	surj_not	[217, 1]	[222, 33]	exact ⟨ true, rfl ⟩	case false ⊢ ∃ a, Bool.not a = false	no goals
https://github.com/kevinsullivan/cs2120f23.git	c2da7c4a6be769c6fca375a54e8c1fa31ba2854b	Instructor/Lectures/grad/sets_relations.lean	not_bij	[224, 1]	[226, 30]	unfold Bijective	⊢ Bijective Bool.not	⊢ Injective Bool.not ∧ Surjective Bool.not
https://github.com/kevinsullivan/cs2120f23.git	c2da7c4a6be769c6fca375a54e8c1fa31ba2854b	Instructor/Lectures/grad/sets_relations.lean	not_bij	[224, 1]	[226, 30]	exact ⟨ inj_not, surj_not ⟩	⊢ Injective Bool.not ∧ Surjective Bool.not	no goals

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We release Lean-Github and InternLM2-Step-Prover with 29K theorems compiled from 100+ Lean 4 repos and a 7B models fine-tuned on Lean-Github and Lean-Workbook with SOTA performance on MiniF2F-test (54.5%), ProofNet (18.1%), and Putnam (5 problems). 🤗Dataset 🤗Model 📑 Paper 📖 README

Citation and Tech Report

@misc{wu2024leangithubcompilinggithublean,
      title={LEAN-GitHub: Compiling GitHub LEAN repositories for a versatile LEAN prover}, 
      author={Zijian Wu and Jiayu Wang and Dahua Lin and Kai Chen},
      year={2024},
      eprint={2407.17227},
      archivePrefix={arXiv},
      primaryClass={cs.AI},
      url={https://arxiv.org/abs/2407.17227}, 
}

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