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 | input stringlengths 73 2.09M |
|---|---|---|---|---|---|---|---|---|---|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Blocks.lean | MulAction.IsBlock_preimage | [261, 1] | [271, 40] | apply Or.intro_left | case inl
G : Type u_4
inst✝³ : Group G
X : Type u_3
inst✝² : MulAction G X
H : Type u_1
Y : Type u_2
inst✝¹ : Group H
inst✝ : MulAction H Y
φ : H → G
j : Y →ₑ[φ] X
B : Set X
hB : IsBlock G B
g : H
heq : φ g • B = B
⊢ g • ⇑j ⁻¹' B = ⇑j ⁻¹' B ∨ Disjoint (g • ⇑j ⁻¹' B) (⇑j ⁻¹' B) | case inl.h
G : Type u_4
inst✝³ : Group G
X : Type u_3
inst✝² : MulAction G X
H : Type u_1
Y : Type u_2
inst✝¹ : Group H
inst✝ : MulAction H Y
φ : H → G
j : Y →ₑ[φ] X
B : Set X
hB : IsBlock G B
g : H
heq : φ g • B = B
⊢ g • ⇑j ⁻¹' B = ⇑j ⁻¹' B | Please generate a tactic in lean4 to solve the state.
STATE:
case inl
G : Type u_4
inst✝³ : Group G
X : Type u_3
inst✝² : MulAction G X
H : Type u_1
Y : Type u_2
inst✝¹ : Group H
inst✝ : MulAction H Y
φ : H → G
j : Y →ₑ[φ] X
B : Set X
hB : IsBlock G B
g : H
heq : φ g • B = B
⊢ g • ⇑j ⁻¹' B = ⇑j ⁻¹' B ∨ Disjoint (g • ⇑j ⁻¹' B) (⇑j ⁻¹' B)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Blocks.lean | MulAction.IsBlock_preimage | [261, 1] | [271, 40] | rw [← Set.preimage_smul_setₑ, heq] | case inl.h
G : Type u_4
inst✝³ : Group G
X : Type u_3
inst✝² : MulAction G X
H : Type u_1
Y : Type u_2
inst✝¹ : Group H
inst✝ : MulAction H Y
φ : H → G
j : Y →ₑ[φ] X
B : Set X
hB : IsBlock G B
g : H
heq : φ g • B = B
⊢ g • ⇑j ⁻¹' B = ⇑j ⁻¹' B | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case inl.h
G : Type u_4
inst✝³ : Group G
X : Type u_3
inst✝² : MulAction G X
H : Type u_1
Y : Type u_2
inst✝¹ : Group H
inst✝ : MulAction H Y
φ : H → G
j : Y →ₑ[φ] X
B : Set X
hB : IsBlock G B
g : H
heq : φ g • B = B
⊢ g • ⇑j ⁻¹' B = ⇑j ⁻¹' B
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Blocks.lean | MulAction.IsBlock_preimage | [261, 1] | [271, 40] | apply Or.intro_right | case inr
G : Type u_4
inst✝³ : Group G
X : Type u_3
inst✝² : MulAction G X
H : Type u_1
Y : Type u_2
inst✝¹ : Group H
inst✝ : MulAction H Y
φ : H → G
j : Y →ₑ[φ] X
B : Set X
hB : IsBlock G B
g : H
hdis : Disjoint (φ g • B) B
⊢ g • ⇑j ⁻¹' B = ⇑j ⁻¹' B ∨ Disjoint (g • ⇑j ⁻¹' B) (⇑j ⁻¹' B) | case inr.h
G : Type u_4
inst✝³ : Group G
X : Type u_3
inst✝² : MulAction G X
H : Type u_1
Y : Type u_2
inst✝¹ : Group H
inst✝ : MulAction H Y
φ : H → G
j : Y →ₑ[φ] X
B : Set X
hB : IsBlock G B
g : H
hdis : Disjoint (φ g • B) B
⊢ Disjoint (g • ⇑j ⁻¹' B) (⇑j ⁻¹' B) | Please generate a tactic in lean4 to solve the state.
STATE:
case inr
G : Type u_4
inst✝³ : Group G
X : Type u_3
inst✝² : MulAction G X
H : Type u_1
Y : Type u_2
inst✝¹ : Group H
inst✝ : MulAction H Y
φ : H → G
j : Y →ₑ[φ] X
B : Set X
hB : IsBlock G B
g : H
hdis : Disjoint (φ g • B) B
⊢ g • ⇑j ⁻¹' B = ⇑j ⁻¹' B ∨ Disjoint (g • ⇑j ⁻¹' B) (⇑j ⁻¹' B)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Blocks.lean | MulAction.IsBlock_preimage | [261, 1] | [271, 40] | rw [← Set.preimage_smul_setₑ] | case inr.h
G : Type u_4
inst✝³ : Group G
X : Type u_3
inst✝² : MulAction G X
H : Type u_1
Y : Type u_2
inst✝¹ : Group H
inst✝ : MulAction H Y
φ : H → G
j : Y →ₑ[φ] X
B : Set X
hB : IsBlock G B
g : H
hdis : Disjoint (φ g • B) B
⊢ Disjoint (g • ⇑j ⁻¹' B) (⇑j ⁻¹' B) | case inr.h
G : Type u_4
inst✝³ : Group G
X : Type u_3
inst✝² : MulAction G X
H : Type u_1
Y : Type u_2
inst✝¹ : Group H
inst✝ : MulAction H Y
φ : H → G
j : Y →ₑ[φ] X
B : Set X
hB : IsBlock G B
g : H
hdis : Disjoint (φ g • B) B
⊢ Disjoint (⇑j ⁻¹' (φ g • B)) (⇑j ⁻¹' B) | Please generate a tactic in lean4 to solve the state.
STATE:
case inr.h
G : Type u_4
inst✝³ : Group G
X : Type u_3
inst✝² : MulAction G X
H : Type u_1
Y : Type u_2
inst✝¹ : Group H
inst✝ : MulAction H Y
φ : H → G
j : Y →ₑ[φ] X
B : Set X
hB : IsBlock G B
g : H
hdis : Disjoint (φ g • B) B
⊢ Disjoint (g • ⇑j ⁻¹' B) (⇑j ⁻¹' B)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Blocks.lean | MulAction.IsBlock_preimage | [261, 1] | [271, 40] | apply Disjoint.preimage | case inr.h
G : Type u_4
inst✝³ : Group G
X : Type u_3
inst✝² : MulAction G X
H : Type u_1
Y : Type u_2
inst✝¹ : Group H
inst✝ : MulAction H Y
φ : H → G
j : Y →ₑ[φ] X
B : Set X
hB : IsBlock G B
g : H
hdis : Disjoint (φ g • B) B
⊢ Disjoint (⇑j ⁻¹' (φ g • B)) (⇑j ⁻¹' B) | case inr.h.h
G : Type u_4
inst✝³ : Group G
X : Type u_3
inst✝² : MulAction G X
H : Type u_1
Y : Type u_2
inst✝¹ : Group H
inst✝ : MulAction H Y
φ : H → G
j : Y →ₑ[φ] X
B : Set X
hB : IsBlock G B
g : H
hdis : Disjoint (φ g • B) B
⊢ Disjoint (φ g • B) B | Please generate a tactic in lean4 to solve the state.
STATE:
case inr.h
G : Type u_4
inst✝³ : Group G
X : Type u_3
inst✝² : MulAction G X
H : Type u_1
Y : Type u_2
inst✝¹ : Group H
inst✝ : MulAction H Y
φ : H → G
j : Y →ₑ[φ] X
B : Set X
hB : IsBlock G B
g : H
hdis : Disjoint (φ g • B) B
⊢ Disjoint (⇑j ⁻¹' (φ g • B)) (⇑j ⁻¹' B)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Blocks.lean | MulAction.IsBlock_preimage | [261, 1] | [271, 40] | exact hdis | case inr.h.h
G : Type u_4
inst✝³ : Group G
X : Type u_3
inst✝² : MulAction G X
H : Type u_1
Y : Type u_2
inst✝¹ : Group H
inst✝ : MulAction H Y
φ : H → G
j : Y →ₑ[φ] X
B : Set X
hB : IsBlock G B
g : H
hdis : Disjoint (φ g • B) B
⊢ Disjoint (φ g • B) B | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case inr.h.h
G : Type u_4
inst✝³ : Group G
X : Type u_3
inst✝² : MulAction G X
H : Type u_1
Y : Type u_2
inst✝¹ : Group H
inst✝ : MulAction H Y
φ : H → G
j : Y →ₑ[φ] X
B : Set X
hB : IsBlock G B
g : H
hdis : Disjoint (φ g • B) B
⊢ Disjoint (φ g • B) B
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Blocks.lean | MulAction.IsBlock_image | [274, 1] | [285, 47] | rw [IsBlock.def] | G : Type u_4
inst✝³ : Group G
X : Type u_3
inst✝² : MulAction G X
H : Type u_1
Y : Type u_2
inst✝¹ : Group H
inst✝ : MulAction H Y
φ : G → H
j : X →ₑ[φ] Y
hφ : Function.Surjective φ
hj : Function.Injective ⇑j
B : Set X
hB : IsBlock G B
⊢ IsBlock H (⇑j '' B) | G : Type u_4
inst✝³ : Group G
X : Type u_3
inst✝² : MulAction G X
H : Type u_1
Y : Type u_2
inst✝¹ : Group H
inst✝ : MulAction H Y
φ : G → H
j : X →ₑ[φ] Y
hφ : Function.Surjective φ
hj : Function.Injective ⇑j
B : Set X
hB : IsBlock G B
⊢ ∀ (g g' : H), g • ⇑j '' B = g' • ⇑j '' B ∨ Disjoint (g • ⇑j '' B) (g' • ⇑j '' B) | Please generate a tactic in lean4 to solve the state.
STATE:
G : Type u_4
inst✝³ : Group G
X : Type u_3
inst✝² : MulAction G X
H : Type u_1
Y : Type u_2
inst✝¹ : Group H
inst✝ : MulAction H Y
φ : G → H
j : X →ₑ[φ] Y
hφ : Function.Surjective φ
hj : Function.Injective ⇑j
B : Set X
hB : IsBlock G B
⊢ IsBlock H (⇑j '' B)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Blocks.lean | MulAction.IsBlock_image | [274, 1] | [285, 47] | intro h h' | G : Type u_4
inst✝³ : Group G
X : Type u_3
inst✝² : MulAction G X
H : Type u_1
Y : Type u_2
inst✝¹ : Group H
inst✝ : MulAction H Y
φ : G → H
j : X →ₑ[φ] Y
hφ : Function.Surjective φ
hj : Function.Injective ⇑j
B : Set X
hB : IsBlock G B
⊢ ∀ (g g' : H), g • ⇑j '' B = g' • ⇑j '' B ∨ Disjoint (g • ⇑j '' B) (g' • ⇑j '' B) | G : Type u_4
inst✝³ : Group G
X : Type u_3
inst✝² : MulAction G X
H : Type u_1
Y : Type u_2
inst✝¹ : Group H
inst✝ : MulAction H Y
φ : G → H
j : X →ₑ[φ] Y
hφ : Function.Surjective φ
hj : Function.Injective ⇑j
B : Set X
hB : IsBlock G B
h h' : H
⊢ h • ⇑j '' B = h' • ⇑j '' B ∨ Disjoint (h • ⇑j '' B) (h' • ⇑j '' B) | Please generate a tactic in lean4 to solve the state.
STATE:
G : Type u_4
inst✝³ : Group G
X : Type u_3
inst✝² : MulAction G X
H : Type u_1
Y : Type u_2
inst✝¹ : Group H
inst✝ : MulAction H Y
φ : G → H
j : X →ₑ[φ] Y
hφ : Function.Surjective φ
hj : Function.Injective ⇑j
B : Set X
hB : IsBlock G B
⊢ ∀ (g g' : H), g • ⇑j '' B = g' • ⇑j '' B ∨ Disjoint (g • ⇑j '' B) (g' • ⇑j '' B)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Blocks.lean | MulAction.IsBlock_image | [274, 1] | [285, 47] | obtain ⟨g, rfl⟩ := hφ h | G : Type u_4
inst✝³ : Group G
X : Type u_3
inst✝² : MulAction G X
H : Type u_1
Y : Type u_2
inst✝¹ : Group H
inst✝ : MulAction H Y
φ : G → H
j : X →ₑ[φ] Y
hφ : Function.Surjective φ
hj : Function.Injective ⇑j
B : Set X
hB : IsBlock G B
h h' : H
⊢ h • ⇑j '' B = h' • ⇑j '' B ∨ Disjoint (h • ⇑j '' B) (h' • ⇑j '' B) | case intro
G : Type u_4
inst✝³ : Group G
X : Type u_3
inst✝² : MulAction G X
H : Type u_1
Y : Type u_2
inst✝¹ : Group H
inst✝ : MulAction H Y
φ : G → H
j : X →ₑ[φ] Y
hφ : Function.Surjective φ
hj : Function.Injective ⇑j
B : Set X
hB : IsBlock G B
h' : H
g : G
⊢ φ g • ⇑j '' B = h' • ⇑j '' B ∨ Disjoint (φ g • ⇑j '' B) (h' • ⇑j '' B) | Please generate a tactic in lean4 to solve the state.
STATE:
G : Type u_4
inst✝³ : Group G
X : Type u_3
inst✝² : MulAction G X
H : Type u_1
Y : Type u_2
inst✝¹ : Group H
inst✝ : MulAction H Y
φ : G → H
j : X →ₑ[φ] Y
hφ : Function.Surjective φ
hj : Function.Injective ⇑j
B : Set X
hB : IsBlock G B
h h' : H
⊢ h • ⇑j '' B = h' • ⇑j '' B ∨ Disjoint (h • ⇑j '' B) (h' • ⇑j '' B)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Blocks.lean | MulAction.IsBlock_image | [274, 1] | [285, 47] | obtain ⟨g', rfl⟩ := hφ h' | case intro
G : Type u_4
inst✝³ : Group G
X : Type u_3
inst✝² : MulAction G X
H : Type u_1
Y : Type u_2
inst✝¹ : Group H
inst✝ : MulAction H Y
φ : G → H
j : X →ₑ[φ] Y
hφ : Function.Surjective φ
hj : Function.Injective ⇑j
B : Set X
hB : IsBlock G B
h' : H
g : G
⊢ φ g • ⇑j '' B = h' • ⇑j '' B ∨ Disjoint (φ g • ⇑j '' B) (h' • ⇑j '' B) | case intro.intro
G : Type u_4
inst✝³ : Group G
X : Type u_3
inst✝² : MulAction G X
H : Type u_1
Y : Type u_2
inst✝¹ : Group H
inst✝ : MulAction H Y
φ : G → H
j : X →ₑ[φ] Y
hφ : Function.Surjective φ
hj : Function.Injective ⇑j
B : Set X
hB : IsBlock G B
g g' : G
⊢ φ g • ⇑j '' B = φ g' • ⇑j '' B ∨ Disjoint (φ g • ⇑j '' B) (φ g' • ⇑j '' B) | Please generate a tactic in lean4 to solve the state.
STATE:
case intro
G : Type u_4
inst✝³ : Group G
X : Type u_3
inst✝² : MulAction G X
H : Type u_1
Y : Type u_2
inst✝¹ : Group H
inst✝ : MulAction H Y
φ : G → H
j : X →ₑ[φ] Y
hφ : Function.Surjective φ
hj : Function.Injective ⇑j
B : Set X
hB : IsBlock G B
h' : H
g : G
⊢ φ g • ⇑j '' B = h' • ⇑j '' B ∨ Disjoint (φ g • ⇑j '' B) (h' • ⇑j '' B)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Blocks.lean | MulAction.IsBlock_image | [274, 1] | [285, 47] | simp only [← Set.image_smul_setₑ] | case intro.intro
G : Type u_4
inst✝³ : Group G
X : Type u_3
inst✝² : MulAction G X
H : Type u_1
Y : Type u_2
inst✝¹ : Group H
inst✝ : MulAction H Y
φ : G → H
j : X →ₑ[φ] Y
hφ : Function.Surjective φ
hj : Function.Injective ⇑j
B : Set X
hB : IsBlock G B
g g' : G
⊢ φ g • ⇑j '' B = φ g' • ⇑j '' B ∨ Disjoint (φ g • ⇑j '' B) (φ g' • ⇑j '' B) | case intro.intro
G : Type u_4
inst✝³ : Group G
X : Type u_3
inst✝² : MulAction G X
H : Type u_1
Y : Type u_2
inst✝¹ : Group H
inst✝ : MulAction H Y
φ : G → H
j : X →ₑ[φ] Y
hφ : Function.Surjective φ
hj : Function.Injective ⇑j
B : Set X
hB : IsBlock G B
g g' : G
⊢ ⇑j '' (g • B) = ⇑j '' (g' • B) ∨ Disjoint (⇑j '' (g • B)) (⇑j '' (g' • B)) | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro
G : Type u_4
inst✝³ : Group G
X : Type u_3
inst✝² : MulAction G X
H : Type u_1
Y : Type u_2
inst✝¹ : Group H
inst✝ : MulAction H Y
φ : G → H
j : X →ₑ[φ] Y
hφ : Function.Surjective φ
hj : Function.Injective ⇑j
B : Set X
hB : IsBlock G B
g g' : G
⊢ φ g • ⇑j '' B = φ g' • ⇑j '' B ∨ Disjoint (φ g • ⇑j '' B) (φ g' • ⇑j '' B)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Blocks.lean | MulAction.IsBlock_image | [274, 1] | [285, 47] | cases' IsBlock.def.mp hB g g' with h h | case intro.intro
G : Type u_4
inst✝³ : Group G
X : Type u_3
inst✝² : MulAction G X
H : Type u_1
Y : Type u_2
inst✝¹ : Group H
inst✝ : MulAction H Y
φ : G → H
j : X →ₑ[φ] Y
hφ : Function.Surjective φ
hj : Function.Injective ⇑j
B : Set X
hB : IsBlock G B
g g' : G
⊢ ⇑j '' (g • B) = ⇑j '' (g' • B) ∨ Disjoint (⇑j '' (g • B)) (⇑j '' (g' • B)) | case intro.intro.inl
G : Type u_4
inst✝³ : Group G
X : Type u_3
inst✝² : MulAction G X
H : Type u_1
Y : Type u_2
inst✝¹ : Group H
inst✝ : MulAction H Y
φ : G → H
j : X →ₑ[φ] Y
hφ : Function.Surjective φ
hj : Function.Injective ⇑j
B : Set X
hB : IsBlock G B
g g' : G
h : g • B = g' • B
⊢ ⇑j '' (g • B) = ⇑j '' (g' • B) ∨ Disjoint (⇑j '' (g • B)) (⇑j '' (g' • B))
case intro.intro.inr
G : Type u_4
inst✝³ : Group G
X : Type u_3
inst✝² : MulAction G X
H : Type u_1
Y : Type u_2
inst✝¹ : Group H
inst✝ : MulAction H Y
φ : G → H
j : X →ₑ[φ] Y
hφ : Function.Surjective φ
hj : Function.Injective ⇑j
B : Set X
hB : IsBlock G B
g g' : G
h : Disjoint (g • B) (g' • B)
⊢ ⇑j '' (g • B) = ⇑j '' (g' • B) ∨ Disjoint (⇑j '' (g • B)) (⇑j '' (g' • B)) | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro
G : Type u_4
inst✝³ : Group G
X : Type u_3
inst✝² : MulAction G X
H : Type u_1
Y : Type u_2
inst✝¹ : Group H
inst✝ : MulAction H Y
φ : G → H
j : X →ₑ[φ] Y
hφ : Function.Surjective φ
hj : Function.Injective ⇑j
B : Set X
hB : IsBlock G B
g g' : G
⊢ ⇑j '' (g • B) = ⇑j '' (g' • B) ∨ Disjoint (⇑j '' (g • B)) (⇑j '' (g' • B))
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Blocks.lean | MulAction.IsBlock_image | [274, 1] | [285, 47] | apply Or.intro_left | case intro.intro.inl
G : Type u_4
inst✝³ : Group G
X : Type u_3
inst✝² : MulAction G X
H : Type u_1
Y : Type u_2
inst✝¹ : Group H
inst✝ : MulAction H Y
φ : G → H
j : X →ₑ[φ] Y
hφ : Function.Surjective φ
hj : Function.Injective ⇑j
B : Set X
hB : IsBlock G B
g g' : G
h : g • B = g' • B
⊢ ⇑j '' (g • B) = ⇑j '' (g' • B) ∨ Disjoint (⇑j '' (g • B)) (⇑j '' (g' • B)) | case intro.intro.inl.h
G : Type u_4
inst✝³ : Group G
X : Type u_3
inst✝² : MulAction G X
H : Type u_1
Y : Type u_2
inst✝¹ : Group H
inst✝ : MulAction H Y
φ : G → H
j : X →ₑ[φ] Y
hφ : Function.Surjective φ
hj : Function.Injective ⇑j
B : Set X
hB : IsBlock G B
g g' : G
h : g • B = g' • B
⊢ ⇑j '' (g • B) = ⇑j '' (g' • B) | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.inl
G : Type u_4
inst✝³ : Group G
X : Type u_3
inst✝² : MulAction G X
H : Type u_1
Y : Type u_2
inst✝¹ : Group H
inst✝ : MulAction H Y
φ : G → H
j : X →ₑ[φ] Y
hφ : Function.Surjective φ
hj : Function.Injective ⇑j
B : Set X
hB : IsBlock G B
g g' : G
h : g • B = g' • B
⊢ ⇑j '' (g • B) = ⇑j '' (g' • B) ∨ Disjoint (⇑j '' (g • B)) (⇑j '' (g' • B))
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Blocks.lean | MulAction.IsBlock_image | [274, 1] | [285, 47] | rw [h] | case intro.intro.inl.h
G : Type u_4
inst✝³ : Group G
X : Type u_3
inst✝² : MulAction G X
H : Type u_1
Y : Type u_2
inst✝¹ : Group H
inst✝ : MulAction H Y
φ : G → H
j : X →ₑ[φ] Y
hφ : Function.Surjective φ
hj : Function.Injective ⇑j
B : Set X
hB : IsBlock G B
g g' : G
h : g • B = g' • B
⊢ ⇑j '' (g • B) = ⇑j '' (g' • B) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.inl.h
G : Type u_4
inst✝³ : Group G
X : Type u_3
inst✝² : MulAction G X
H : Type u_1
Y : Type u_2
inst✝¹ : Group H
inst✝ : MulAction H Y
φ : G → H
j : X →ₑ[φ] Y
hφ : Function.Surjective φ
hj : Function.Injective ⇑j
B : Set X
hB : IsBlock G B
g g' : G
h : g • B = g' • B
⊢ ⇑j '' (g • B) = ⇑j '' (g' • B)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Blocks.lean | MulAction.IsBlock_image | [274, 1] | [285, 47] | apply Or.intro_right | case intro.intro.inr
G : Type u_4
inst✝³ : Group G
X : Type u_3
inst✝² : MulAction G X
H : Type u_1
Y : Type u_2
inst✝¹ : Group H
inst✝ : MulAction H Y
φ : G → H
j : X →ₑ[φ] Y
hφ : Function.Surjective φ
hj : Function.Injective ⇑j
B : Set X
hB : IsBlock G B
g g' : G
h : Disjoint (g • B) (g' • B)
⊢ ⇑j '' (g • B) = ⇑j '' (g' • B) ∨ Disjoint (⇑j '' (g • B)) (⇑j '' (g' • B)) | case intro.intro.inr.h
G : Type u_4
inst✝³ : Group G
X : Type u_3
inst✝² : MulAction G X
H : Type u_1
Y : Type u_2
inst✝¹ : Group H
inst✝ : MulAction H Y
φ : G → H
j : X →ₑ[φ] Y
hφ : Function.Surjective φ
hj : Function.Injective ⇑j
B : Set X
hB : IsBlock G B
g g' : G
h : Disjoint (g • B) (g' • B)
⊢ Disjoint (⇑j '' (g • B)) (⇑j '' (g' • B)) | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.inr
G : Type u_4
inst✝³ : Group G
X : Type u_3
inst✝² : MulAction G X
H : Type u_1
Y : Type u_2
inst✝¹ : Group H
inst✝ : MulAction H Y
φ : G → H
j : X →ₑ[φ] Y
hφ : Function.Surjective φ
hj : Function.Injective ⇑j
B : Set X
hB : IsBlock G B
g g' : G
h : Disjoint (g • B) (g' • B)
⊢ ⇑j '' (g • B) = ⇑j '' (g' • B) ∨ Disjoint (⇑j '' (g • B)) (⇑j '' (g' • B))
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Blocks.lean | MulAction.IsBlock_image | [274, 1] | [285, 47] | exact Set.disjoint_image_of_injective hj h | case intro.intro.inr.h
G : Type u_4
inst✝³ : Group G
X : Type u_3
inst✝² : MulAction G X
H : Type u_1
Y : Type u_2
inst✝¹ : Group H
inst✝ : MulAction H Y
φ : G → H
j : X →ₑ[φ] Y
hφ : Function.Surjective φ
hj : Function.Injective ⇑j
B : Set X
hB : IsBlock G B
g g' : G
h : Disjoint (g • B) (g' • B)
⊢ Disjoint (⇑j '' (g • B)) (⇑j '' (g' • B)) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.inr.h
G : Type u_4
inst✝³ : Group G
X : Type u_3
inst✝² : MulAction G X
H : Type u_1
Y : Type u_2
inst✝¹ : Group H
inst✝ : MulAction H Y
φ : G → H
j : X →ₑ[φ] Y
hφ : Function.Surjective φ
hj : Function.Injective ⇑j
B : Set X
hB : IsBlock G B
g g' : G
h : Disjoint (g • B) (g' • B)
⊢ Disjoint (⇑j '' (g • B)) (⇑j '' (g' • B))
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Blocks.lean | MulAction.SubMulAction.smul_coe_eq_coe_smul | [294, 1] | [308, 28] | ext | G : Type u_1
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
C : SubMulAction G X
B : Set ↥C
g : G
⊢ g • Subtype.val '' B = Subtype.val '' (g • B) | case h
G : Type u_1
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
C : SubMulAction G X
B : Set ↥C
g : G
x✝ : X
⊢ x✝ ∈ g • Subtype.val '' B ↔ x✝ ∈ Subtype.val '' (g • B) | Please generate a tactic in lean4 to solve the state.
STATE:
G : Type u_1
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
C : SubMulAction G X
B : Set ↥C
g : G
⊢ g • Subtype.val '' B = Subtype.val '' (g • B)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Blocks.lean | MulAction.SubMulAction.smul_coe_eq_coe_smul | [294, 1] | [308, 28] | constructor | case h
G : Type u_1
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
C : SubMulAction G X
B : Set ↥C
g : G
x✝ : X
⊢ x✝ ∈ g • Subtype.val '' B ↔ x✝ ∈ Subtype.val '' (g • B) | case h.mp
G : Type u_1
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
C : SubMulAction G X
B : Set ↥C
g : G
x✝ : X
⊢ x✝ ∈ g • Subtype.val '' B → x✝ ∈ Subtype.val '' (g • B)
case h.mpr
G : Type u_1
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
C : SubMulAction G X
B : Set ↥C
g : G
x✝ : X
⊢ x✝ ∈ Subtype.val '' (g • B) → x✝ ∈ g • Subtype.val '' B | Please generate a tactic in lean4 to solve the state.
STATE:
case h
G : Type u_1
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
C : SubMulAction G X
B : Set ↥C
g : G
x✝ : X
⊢ x✝ ∈ g • Subtype.val '' B ↔ x✝ ∈ Subtype.val '' (g • B)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Blocks.lean | MulAction.SubMulAction.smul_coe_eq_coe_smul | [294, 1] | [308, 28] | intro hx | case h.mp
G : Type u_1
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
C : SubMulAction G X
B : Set ↥C
g : G
x✝ : X
⊢ x✝ ∈ g • Subtype.val '' B → x✝ ∈ Subtype.val '' (g • B) | case h.mp
G : Type u_1
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
C : SubMulAction G X
B : Set ↥C
g : G
x✝ : X
hx : x✝ ∈ g • Subtype.val '' B
⊢ x✝ ∈ Subtype.val '' (g • B) | Please generate a tactic in lean4 to solve the state.
STATE:
case h.mp
G : Type u_1
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
C : SubMulAction G X
B : Set ↥C
g : G
x✝ : X
⊢ x✝ ∈ g • Subtype.val '' B → x✝ ∈ Subtype.val '' (g • B)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Blocks.lean | MulAction.SubMulAction.smul_coe_eq_coe_smul | [294, 1] | [308, 28] | obtain ⟨y, hy, rfl⟩ := hx | case h.mp
G : Type u_1
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
C : SubMulAction G X
B : Set ↥C
g : G
x✝ : X
hx : x✝ ∈ g • Subtype.val '' B
⊢ x✝ ∈ Subtype.val '' (g • B) | case h.mp.intro.intro
G : Type u_1
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
C : SubMulAction G X
B : Set ↥C
g : G
y : X
hy : y ∈ Subtype.val '' B
⊢ (fun x => g • x) y ∈ Subtype.val '' (g • B) | Please generate a tactic in lean4 to solve the state.
STATE:
case h.mp
G : Type u_1
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
C : SubMulAction G X
B : Set ↥C
g : G
x✝ : X
hx : x✝ ∈ g • Subtype.val '' B
⊢ x✝ ∈ Subtype.val '' (g • B)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Blocks.lean | MulAction.SubMulAction.smul_coe_eq_coe_smul | [294, 1] | [308, 28] | obtain ⟨z, hz, rfl⟩ := hy | case h.mp.intro.intro
G : Type u_1
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
C : SubMulAction G X
B : Set ↥C
g : G
y : X
hy : y ∈ Subtype.val '' B
⊢ (fun x => g • x) y ∈ Subtype.val '' (g • B) | case h.mp.intro.intro.intro.intro
G : Type u_1
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
C : SubMulAction G X
B : Set ↥C
g : G
z : ↥C
hz : z ∈ B
⊢ (fun x => g • x) ↑z ∈ Subtype.val '' (g • B) | Please generate a tactic in lean4 to solve the state.
STATE:
case h.mp.intro.intro
G : Type u_1
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
C : SubMulAction G X
B : Set ↥C
g : G
y : X
hy : y ∈ Subtype.val '' B
⊢ (fun x => g • x) y ∈ Subtype.val '' (g • B)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Blocks.lean | MulAction.SubMulAction.smul_coe_eq_coe_smul | [294, 1] | [308, 28] | use g • z | case h.mp.intro.intro.intro.intro
G : Type u_1
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
C : SubMulAction G X
B : Set ↥C
g : G
z : ↥C
hz : z ∈ B
⊢ (fun x => g • x) ↑z ∈ Subtype.val '' (g • B) | case h
G : Type u_1
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
C : SubMulAction G X
B : Set ↥C
g : G
z : ↥C
hz : z ∈ B
⊢ g • z ∈ g • B ∧ ↑(g • z) = (fun x => g • x) ↑z | Please generate a tactic in lean4 to solve the state.
STATE:
case h.mp.intro.intro.intro.intro
G : Type u_1
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
C : SubMulAction G X
B : Set ↥C
g : G
z : ↥C
hz : z ∈ B
⊢ (fun x => g • x) ↑z ∈ Subtype.val '' (g • B)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Blocks.lean | MulAction.SubMulAction.smul_coe_eq_coe_smul | [294, 1] | [308, 28] | constructor | case h
G : Type u_1
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
C : SubMulAction G X
B : Set ↥C
g : G
z : ↥C
hz : z ∈ B
⊢ g • z ∈ g • B ∧ ↑(g • z) = (fun x => g • x) ↑z | case h.left
G : Type u_1
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
C : SubMulAction G X
B : Set ↥C
g : G
z : ↥C
hz : z ∈ B
⊢ g • z ∈ g • B
case h.right
G : Type u_1
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
C : SubMulAction G X
B : Set ↥C
g : G
z : ↥C
hz : z ∈ B
⊢ ↑(g • z) = (fun x => g • x) ↑z | Please generate a tactic in lean4 to solve the state.
STATE:
case h
G : Type u_1
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
C : SubMulAction G X
B : Set ↥C
g : G
z : ↥C
hz : z ∈ B
⊢ g • z ∈ g • B ∧ ↑(g • z) = (fun x => g • x) ↑z
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Blocks.lean | MulAction.SubMulAction.smul_coe_eq_coe_smul | [294, 1] | [308, 28] | exact ⟨z, hz, rfl⟩ | case h.left
G : Type u_1
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
C : SubMulAction G X
B : Set ↥C
g : G
z : ↥C
hz : z ∈ B
⊢ g • z ∈ g • B
case h.right
G : Type u_1
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
C : SubMulAction G X
B : Set ↥C
g : G
z : ↥C
hz : z ∈ B
⊢ ↑(g • z) = (fun x => g • x) ↑z | case h.right
G : Type u_1
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
C : SubMulAction G X
B : Set ↥C
g : G
z : ↥C
hz : z ∈ B
⊢ ↑(g • z) = (fun x => g • x) ↑z | Please generate a tactic in lean4 to solve the state.
STATE:
case h.left
G : Type u_1
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
C : SubMulAction G X
B : Set ↥C
g : G
z : ↥C
hz : z ∈ B
⊢ g • z ∈ g • B
case h.right
G : Type u_1
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
C : SubMulAction G X
B : Set ↥C
g : G
z : ↥C
hz : z ∈ B
⊢ ↑(g • z) = (fun x => g • x) ↑z
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Blocks.lean | MulAction.SubMulAction.smul_coe_eq_coe_smul | [294, 1] | [308, 28] | rw [SubMulAction.val_smul_of_tower] | case h.right
G : Type u_1
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
C : SubMulAction G X
B : Set ↥C
g : G
z : ↥C
hz : z ∈ B
⊢ ↑(g • z) = (fun x => g • x) ↑z | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h.right
G : Type u_1
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
C : SubMulAction G X
B : Set ↥C
g : G
z : ↥C
hz : z ∈ B
⊢ ↑(g • z) = (fun x => g • x) ↑z
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Blocks.lean | MulAction.SubMulAction.smul_coe_eq_coe_smul | [294, 1] | [308, 28] | intro hx | case h.mpr
G : Type u_1
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
C : SubMulAction G X
B : Set ↥C
g : G
x✝ : X
⊢ x✝ ∈ Subtype.val '' (g • B) → x✝ ∈ g • Subtype.val '' B | case h.mpr
G : Type u_1
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
C : SubMulAction G X
B : Set ↥C
g : G
x✝ : X
hx : x✝ ∈ Subtype.val '' (g • B)
⊢ x✝ ∈ g • Subtype.val '' B | Please generate a tactic in lean4 to solve the state.
STATE:
case h.mpr
G : Type u_1
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
C : SubMulAction G X
B : Set ↥C
g : G
x✝ : X
⊢ x✝ ∈ Subtype.val '' (g • B) → x✝ ∈ g • Subtype.val '' B
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Blocks.lean | MulAction.SubMulAction.smul_coe_eq_coe_smul | [294, 1] | [308, 28] | obtain ⟨y, hy, rfl⟩ := hx | case h.mpr
G : Type u_1
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
C : SubMulAction G X
B : Set ↥C
g : G
x✝ : X
hx : x✝ ∈ Subtype.val '' (g • B)
⊢ x✝ ∈ g • Subtype.val '' B | case h.mpr.intro.intro
G : Type u_1
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
C : SubMulAction G X
B : Set ↥C
g : G
y : ↥C
hy : y ∈ g • B
⊢ ↑y ∈ g • Subtype.val '' B | Please generate a tactic in lean4 to solve the state.
STATE:
case h.mpr
G : Type u_1
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
C : SubMulAction G X
B : Set ↥C
g : G
x✝ : X
hx : x✝ ∈ Subtype.val '' (g • B)
⊢ x✝ ∈ g • Subtype.val '' B
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Blocks.lean | MulAction.SubMulAction.smul_coe_eq_coe_smul | [294, 1] | [308, 28] | obtain ⟨z, hz, rfl⟩ := hy | case h.mpr.intro.intro
G : Type u_1
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
C : SubMulAction G X
B : Set ↥C
g : G
y : ↥C
hy : y ∈ g • B
⊢ ↑y ∈ g • Subtype.val '' B | case h.mpr.intro.intro.intro.intro
G : Type u_1
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
C : SubMulAction G X
B : Set ↥C
g : G
z : ↥C
hz : z ∈ B
⊢ ↑((fun x => g • x) z) ∈ g • Subtype.val '' B | Please generate a tactic in lean4 to solve the state.
STATE:
case h.mpr.intro.intro
G : Type u_1
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
C : SubMulAction G X
B : Set ↥C
g : G
y : ↥C
hy : y ∈ g • B
⊢ ↑y ∈ g • Subtype.val '' B
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Blocks.lean | MulAction.SubMulAction.smul_coe_eq_coe_smul | [294, 1] | [308, 28] | rw [SubMulAction.val_smul_of_tower] | case h.mpr.intro.intro.intro.intro
G : Type u_1
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
C : SubMulAction G X
B : Set ↥C
g : G
z : ↥C
hz : z ∈ B
⊢ ↑((fun x => g • x) z) ∈ g • Subtype.val '' B | case h.mpr.intro.intro.intro.intro
G : Type u_1
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
C : SubMulAction G X
B : Set ↥C
g : G
z : ↥C
hz : z ∈ B
⊢ g • ↑z ∈ g • Subtype.val '' B | Please generate a tactic in lean4 to solve the state.
STATE:
case h.mpr.intro.intro.intro.intro
G : Type u_1
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
C : SubMulAction G X
B : Set ↥C
g : G
z : ↥C
hz : z ∈ B
⊢ ↑((fun x => g • x) z) ∈ g • Subtype.val '' B
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Blocks.lean | MulAction.SubMulAction.smul_coe_eq_coe_smul | [294, 1] | [308, 28] | use ↑z | case h.mpr.intro.intro.intro.intro
G : Type u_1
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
C : SubMulAction G X
B : Set ↥C
g : G
z : ↥C
hz : z ∈ B
⊢ g • ↑z ∈ g • Subtype.val '' B | case h
G : Type u_1
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
C : SubMulAction G X
B : Set ↥C
g : G
z : ↥C
hz : z ∈ B
⊢ ↑z ∈ Subtype.val '' B ∧ (fun x => g • x) ↑z = g • ↑z | Please generate a tactic in lean4 to solve the state.
STATE:
case h.mpr.intro.intro.intro.intro
G : Type u_1
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
C : SubMulAction G X
B : Set ↥C
g : G
z : ↥C
hz : z ∈ B
⊢ g • ↑z ∈ g • Subtype.val '' B
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Blocks.lean | MulAction.SubMulAction.smul_coe_eq_coe_smul | [294, 1] | [308, 28] | constructor | case h
G : Type u_1
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
C : SubMulAction G X
B : Set ↥C
g : G
z : ↥C
hz : z ∈ B
⊢ ↑z ∈ Subtype.val '' B ∧ (fun x => g • x) ↑z = g • ↑z | case h.left
G : Type u_1
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
C : SubMulAction G X
B : Set ↥C
g : G
z : ↥C
hz : z ∈ B
⊢ ↑z ∈ Subtype.val '' B
case h.right
G : Type u_1
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
C : SubMulAction G X
B : Set ↥C
g : G
z : ↥C
hz : z ∈ B
⊢ (fun x => g • x) ↑z = g • ↑z | Please generate a tactic in lean4 to solve the state.
STATE:
case h
G : Type u_1
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
C : SubMulAction G X
B : Set ↥C
g : G
z : ↥C
hz : z ∈ B
⊢ ↑z ∈ Subtype.val '' B ∧ (fun x => g • x) ↑z = g • ↑z
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Blocks.lean | MulAction.SubMulAction.smul_coe_eq_coe_smul | [294, 1] | [308, 28] | exact ⟨z, hz, rfl⟩ | case h.left
G : Type u_1
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
C : SubMulAction G X
B : Set ↥C
g : G
z : ↥C
hz : z ∈ B
⊢ ↑z ∈ Subtype.val '' B
case h.right
G : Type u_1
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
C : SubMulAction G X
B : Set ↥C
g : G
z : ↥C
hz : z ∈ B
⊢ (fun x => g • x) ↑z = g • ↑z | case h.right
G : Type u_1
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
C : SubMulAction G X
B : Set ↥C
g : G
z : ↥C
hz : z ∈ B
⊢ (fun x => g • x) ↑z = g • ↑z | Please generate a tactic in lean4 to solve the state.
STATE:
case h.left
G : Type u_1
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
C : SubMulAction G X
B : Set ↥C
g : G
z : ↥C
hz : z ∈ B
⊢ ↑z ∈ Subtype.val '' B
case h.right
G : Type u_1
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
C : SubMulAction G X
B : Set ↥C
g : G
z : ↥C
hz : z ∈ B
⊢ (fun x => g • x) ↑z = g • ↑z
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Blocks.lean | MulAction.SubMulAction.smul_coe_eq_coe_smul | [294, 1] | [308, 28] | rfl | case h.right
G : Type u_1
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
C : SubMulAction G X
B : Set ↥C
g : G
z : ↥C
hz : z ∈ B
⊢ (fun x => g • x) ↑z = g • ↑z | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h.right
G : Type u_1
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
C : SubMulAction G X
B : Set ↥C
g : G
z : ↥C
hz : z ∈ B
⊢ (fun x => g • x) ↑z = g • ↑z
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Blocks.lean | MulAction.SubMulAction.IsBlock_coe | [311, 1] | [323, 33] | simp only [IsBlock.def_one] | G : Type u_1
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
C : SubMulAction G X
B : Set ↥C
⊢ MulAction.IsBlock G B ↔ MulAction.IsBlock G (Subtype.val '' B) | G : Type u_1
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
C : SubMulAction G X
B : Set ↥C
⊢ (∀ (g : G), g • B = B ∨ Disjoint (g • B) B) ↔
∀ (g : G), g • Subtype.val '' B = Subtype.val '' B ∨ Disjoint (g • Subtype.val '' B) (Subtype.val '' B) | Please generate a tactic in lean4 to solve the state.
STATE:
G : Type u_1
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
C : SubMulAction G X
B : Set ↥C
⊢ MulAction.IsBlock G B ↔ MulAction.IsBlock G (Subtype.val '' B)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Blocks.lean | MulAction.SubMulAction.IsBlock_coe | [311, 1] | [323, 33] | apply forall_congr' | G : Type u_1
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
C : SubMulAction G X
B : Set ↥C
⊢ (∀ (g : G), g • B = B ∨ Disjoint (g • B) B) ↔
∀ (g : G), g • Subtype.val '' B = Subtype.val '' B ∨ Disjoint (g • Subtype.val '' B) (Subtype.val '' B) | case h
G : Type u_1
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
C : SubMulAction G X
B : Set ↥C
⊢ ∀ (a : G),
a • B = B ∨ Disjoint (a • B) B ↔
a • Subtype.val '' B = Subtype.val '' B ∨ Disjoint (a • Subtype.val '' B) (Subtype.val '' B) | Please generate a tactic in lean4 to solve the state.
STATE:
G : Type u_1
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
C : SubMulAction G X
B : Set ↥C
⊢ (∀ (g : G), g • B = B ∨ Disjoint (g • B) B) ↔
∀ (g : G), g • Subtype.val '' B = Subtype.val '' B ∨ Disjoint (g • Subtype.val '' B) (Subtype.val '' B)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Blocks.lean | MulAction.SubMulAction.IsBlock_coe | [311, 1] | [323, 33] | intro g | case h
G : Type u_1
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
C : SubMulAction G X
B : Set ↥C
⊢ ∀ (a : G),
a • B = B ∨ Disjoint (a • B) B ↔
a • Subtype.val '' B = Subtype.val '' B ∨ Disjoint (a • Subtype.val '' B) (Subtype.val '' B) | case h
G : Type u_1
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
C : SubMulAction G X
B : Set ↥C
g : G
⊢ g • B = B ∨ Disjoint (g • B) B ↔
g • Subtype.val '' B = Subtype.val '' B ∨ Disjoint (g • Subtype.val '' B) (Subtype.val '' B) | Please generate a tactic in lean4 to solve the state.
STATE:
case h
G : Type u_1
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
C : SubMulAction G X
B : Set ↥C
⊢ ∀ (a : G),
a • B = B ∨ Disjoint (a • B) B ↔
a • Subtype.val '' B = Subtype.val '' B ∨ Disjoint (a • Subtype.val '' B) (Subtype.val '' B)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Blocks.lean | MulAction.SubMulAction.IsBlock_coe | [311, 1] | [323, 33] | rw [SubMulAction.smul_coe_eq_coe_smul] | case h
G : Type u_1
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
C : SubMulAction G X
B : Set ↥C
g : G
⊢ g • B = B ∨ Disjoint (g • B) B ↔
g • Subtype.val '' B = Subtype.val '' B ∨ Disjoint (g • Subtype.val '' B) (Subtype.val '' B) | case h
G : Type u_1
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
C : SubMulAction G X
B : Set ↥C
g : G
⊢ g • B = B ∨ Disjoint (g • B) B ↔
Subtype.val '' (g • B) = Subtype.val '' B ∨ Disjoint (Subtype.val '' (g • B)) (Subtype.val '' B) | Please generate a tactic in lean4 to solve the state.
STATE:
case h
G : Type u_1
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
C : SubMulAction G X
B : Set ↥C
g : G
⊢ g • B = B ∨ Disjoint (g • B) B ↔
g • Subtype.val '' B = Subtype.val '' B ∨ Disjoint (g • Subtype.val '' B) (Subtype.val '' B)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Blocks.lean | MulAction.SubMulAction.IsBlock_coe | [311, 1] | [323, 33] | apply or_congr (Set.image_eq_image Subtype.coe_injective).symm | case h
G : Type u_1
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
C : SubMulAction G X
B : Set ↥C
g : G
⊢ g • B = B ∨ Disjoint (g • B) B ↔
Subtype.val '' (g • B) = Subtype.val '' B ∨ Disjoint (Subtype.val '' (g • B)) (Subtype.val '' B) | case h
G : Type u_1
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
C : SubMulAction G X
B : Set ↥C
g : G
⊢ Disjoint (g • B) B ↔ Disjoint (Subtype.val '' (g • B)) (Subtype.val '' B) | Please generate a tactic in lean4 to solve the state.
STATE:
case h
G : Type u_1
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
C : SubMulAction G X
B : Set ↥C
g : G
⊢ g • B = B ∨ Disjoint (g • B) B ↔
Subtype.val '' (g • B) = Subtype.val '' B ∨ Disjoint (Subtype.val '' (g • B)) (Subtype.val '' B)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Blocks.lean | MulAction.SubMulAction.IsBlock_coe | [311, 1] | [323, 33] | simp only [Set.disjoint_iff, Set.subset_empty_iff] | case h
G : Type u_1
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
C : SubMulAction G X
B : Set ↥C
g : G
⊢ Disjoint (g • B) B ↔ Disjoint (Subtype.val '' (g • B)) (Subtype.val '' B) | case h
G : Type u_1
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
C : SubMulAction G X
B : Set ↥C
g : G
⊢ g • B ∩ B = ∅ ↔ Subtype.val '' (g • B) ∩ Subtype.val '' B = ∅ | Please generate a tactic in lean4 to solve the state.
STATE:
case h
G : Type u_1
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
C : SubMulAction G X
B : Set ↥C
g : G
⊢ Disjoint (g • B) B ↔ Disjoint (Subtype.val '' (g • B)) (Subtype.val '' B)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Blocks.lean | MulAction.SubMulAction.IsBlock_coe | [311, 1] | [323, 33] | rw [←
Set.InjOn.image_inter (Set.injOn_of_injective Subtype.coe_injective _) (Set.subset_univ _)
(Set.subset_univ _)] | case h
G : Type u_1
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
C : SubMulAction G X
B : Set ↥C
g : G
⊢ g • B ∩ B = ∅ ↔ Subtype.val '' (g • B) ∩ Subtype.val '' B = ∅ | case h
G : Type u_1
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
C : SubMulAction G X
B : Set ↥C
g : G
⊢ g • B ∩ B = ∅ ↔ (fun a => ↑a) '' (g • B ∩ B) = ∅ | Please generate a tactic in lean4 to solve the state.
STATE:
case h
G : Type u_1
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
C : SubMulAction G X
B : Set ↥C
g : G
⊢ g • B ∩ B = ∅ ↔ Subtype.val '' (g • B) ∩ Subtype.val '' B = ∅
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Blocks.lean | MulAction.SubMulAction.IsBlock_coe | [311, 1] | [323, 33] | simp only [Set.image_eq_empty] | case h
G : Type u_1
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
C : SubMulAction G X
B : Set ↥C
g : G
⊢ g • B ∩ B = ∅ ↔ (fun a => ↑a) '' (g • B ∩ B) = ∅ | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h
G : Type u_1
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
C : SubMulAction G X
B : Set ↥C
g : G
⊢ g • B ∩ B = ∅ ↔ (fun a => ↑a) '' (g • B ∩ B) = ∅
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Blocks.lean | MulAction.IsBlock.of_top_iff | [326, 1] | [331, 45] | simp only [IsBlock.def_one] | G : Type u_2
inst✝¹ : Group G
X : Type u_1
inst✝ : MulAction G X
B : Set X
⊢ IsBlock G B ↔ IsBlock (↥⊤) B | G : Type u_2
inst✝¹ : Group G
X : Type u_1
inst✝ : MulAction G X
B : Set X
⊢ (∀ (g : G), g • B = B ∨ Disjoint (g • B) B) ↔ ∀ (g : ↥⊤), g • B = B ∨ Disjoint (g • B) B | Please generate a tactic in lean4 to solve the state.
STATE:
G : Type u_2
inst✝¹ : Group G
X : Type u_1
inst✝ : MulAction G X
B : Set X
⊢ IsBlock G B ↔ IsBlock (↥⊤) B
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Blocks.lean | MulAction.IsBlock.of_top_iff | [326, 1] | [331, 45] | constructor | G : Type u_2
inst✝¹ : Group G
X : Type u_1
inst✝ : MulAction G X
B : Set X
⊢ (∀ (g : G), g • B = B ∨ Disjoint (g • B) B) ↔ ∀ (g : ↥⊤), g • B = B ∨ Disjoint (g • B) B | case mp
G : Type u_2
inst✝¹ : Group G
X : Type u_1
inst✝ : MulAction G X
B : Set X
⊢ (∀ (g : G), g • B = B ∨ Disjoint (g • B) B) → ∀ (g : ↥⊤), g • B = B ∨ Disjoint (g • B) B
case mpr
G : Type u_2
inst✝¹ : Group G
X : Type u_1
inst✝ : MulAction G X
B : Set X
⊢ (∀ (g : ↥⊤), g • B = B ∨ Disjoint (g • B) B) → ∀ (g : G), g • B = B ∨ Disjoint (g • B) B | Please generate a tactic in lean4 to solve the state.
STATE:
G : Type u_2
inst✝¹ : Group G
X : Type u_1
inst✝ : MulAction G X
B : Set X
⊢ (∀ (g : G), g • B = B ∨ Disjoint (g • B) B) ↔ ∀ (g : ↥⊤), g • B = B ∨ Disjoint (g • B) B
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Blocks.lean | MulAction.IsBlock.of_top_iff | [326, 1] | [331, 45] | intro h g | case mp
G : Type u_2
inst✝¹ : Group G
X : Type u_1
inst✝ : MulAction G X
B : Set X
⊢ (∀ (g : G), g • B = B ∨ Disjoint (g • B) B) → ∀ (g : ↥⊤), g • B = B ∨ Disjoint (g • B) B
case mpr
G : Type u_2
inst✝¹ : Group G
X : Type u_1
inst✝ : MulAction G X
B : Set X
⊢ (∀ (g : ↥⊤), g • B = B ∨ Disjoint (g • B) B) → ∀ (g : G), g • B = B ∨ Disjoint (g • B) B | case mp
G : Type u_2
inst✝¹ : Group G
X : Type u_1
inst✝ : MulAction G X
B : Set X
h : ∀ (g : G), g • B = B ∨ Disjoint (g • B) B
g : ↥⊤
⊢ g • B = B ∨ Disjoint (g • B) B
case mpr
G : Type u_2
inst✝¹ : Group G
X : Type u_1
inst✝ : MulAction G X
B : Set X
⊢ (∀ (g : ↥⊤), g • B = B ∨ Disjoint (g • B) B) → ∀ (g : G), g • B = B ∨ Disjoint (g • B) B | Please generate a tactic in lean4 to solve the state.
STATE:
case mp
G : Type u_2
inst✝¹ : Group G
X : Type u_1
inst✝ : MulAction G X
B : Set X
⊢ (∀ (g : G), g • B = B ∨ Disjoint (g • B) B) → ∀ (g : ↥⊤), g • B = B ∨ Disjoint (g • B) B
case mpr
G : Type u_2
inst✝¹ : Group G
X : Type u_1
inst✝ : MulAction G X
B : Set X
⊢ (∀ (g : ↥⊤), g • B = B ∨ Disjoint (g • B) B) → ∀ (g : G), g • B = B ∨ Disjoint (g • B) B
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Blocks.lean | MulAction.IsBlock.of_top_iff | [326, 1] | [331, 45] | exact h g | case mp
G : Type u_2
inst✝¹ : Group G
X : Type u_1
inst✝ : MulAction G X
B : Set X
h : ∀ (g : G), g • B = B ∨ Disjoint (g • B) B
g : ↥⊤
⊢ g • B = B ∨ Disjoint (g • B) B
case mpr
G : Type u_2
inst✝¹ : Group G
X : Type u_1
inst✝ : MulAction G X
B : Set X
⊢ (∀ (g : ↥⊤), g • B = B ∨ Disjoint (g • B) B) → ∀ (g : G), g • B = B ∨ Disjoint (g • B) B | case mpr
G : Type u_2
inst✝¹ : Group G
X : Type u_1
inst✝ : MulAction G X
B : Set X
⊢ (∀ (g : ↥⊤), g • B = B ∨ Disjoint (g • B) B) → ∀ (g : G), g • B = B ∨ Disjoint (g • B) B | Please generate a tactic in lean4 to solve the state.
STATE:
case mp
G : Type u_2
inst✝¹ : Group G
X : Type u_1
inst✝ : MulAction G X
B : Set X
h : ∀ (g : G), g • B = B ∨ Disjoint (g • B) B
g : ↥⊤
⊢ g • B = B ∨ Disjoint (g • B) B
case mpr
G : Type u_2
inst✝¹ : Group G
X : Type u_1
inst✝ : MulAction G X
B : Set X
⊢ (∀ (g : ↥⊤), g • B = B ∨ Disjoint (g • B) B) → ∀ (g : G), g • B = B ∨ Disjoint (g • B) B
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Blocks.lean | MulAction.IsBlock.of_top_iff | [326, 1] | [331, 45] | intro h g | case mpr
G : Type u_2
inst✝¹ : Group G
X : Type u_1
inst✝ : MulAction G X
B : Set X
⊢ (∀ (g : ↥⊤), g • B = B ∨ Disjoint (g • B) B) → ∀ (g : G), g • B = B ∨ Disjoint (g • B) B | case mpr
G : Type u_2
inst✝¹ : Group G
X : Type u_1
inst✝ : MulAction G X
B : Set X
h : ∀ (g : ↥⊤), g • B = B ∨ Disjoint (g • B) B
g : G
⊢ g • B = B ∨ Disjoint (g • B) B | Please generate a tactic in lean4 to solve the state.
STATE:
case mpr
G : Type u_2
inst✝¹ : Group G
X : Type u_1
inst✝ : MulAction G X
B : Set X
⊢ (∀ (g : ↥⊤), g • B = B ∨ Disjoint (g • B) B) → ∀ (g : G), g • B = B ∨ Disjoint (g • B) B
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Blocks.lean | MulAction.IsBlock.of_top_iff | [326, 1] | [331, 45] | exact h ⟨g, Subgroup.mem_top g⟩ | case mpr
G : Type u_2
inst✝¹ : Group G
X : Type u_1
inst✝ : MulAction G X
B : Set X
h : ∀ (g : ↥⊤), g • B = B ∨ Disjoint (g • B) B
g : G
⊢ g • B = B ∨ Disjoint (g • B) B | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case mpr
G : Type u_2
inst✝¹ : Group G
X : Type u_1
inst✝ : MulAction G X
B : Set X
h : ∀ (g : ↥⊤), g • B = B ∨ Disjoint (g • B) B
g : G
⊢ g • B = B ∨ Disjoint (g • B) B
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Blocks.lean | MulAction.orbit.equal_or_disjoint | [334, 1] | [343, 20] | cases' em (Disjoint (orbit G a) (orbit G b)) with h h | G : Type u_2
inst✝¹ : Group G
X : Type u_1
inst✝ : MulAction G X
a b : X
⊢ orbit G a = orbit G b ∨ Disjoint (orbit G a) (orbit G b) | case inl
G : Type u_2
inst✝¹ : Group G
X : Type u_1
inst✝ : MulAction G X
a b : X
h : Disjoint (orbit G a) (orbit G b)
⊢ orbit G a = orbit G b ∨ Disjoint (orbit G a) (orbit G b)
case inr
G : Type u_2
inst✝¹ : Group G
X : Type u_1
inst✝ : MulAction G X
a b : X
h : ¬Disjoint (orbit G a) (orbit G b)
⊢ orbit G a = orbit G b ∨ Disjoint (orbit G a) (orbit G b) | Please generate a tactic in lean4 to solve the state.
STATE:
G : Type u_2
inst✝¹ : Group G
X : Type u_1
inst✝ : MulAction G X
a b : X
⊢ orbit G a = orbit G b ∨ Disjoint (orbit G a) (orbit G b)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Blocks.lean | MulAction.orbit.equal_or_disjoint | [334, 1] | [343, 20] | apply Or.intro_left | case inr
G : Type u_2
inst✝¹ : Group G
X : Type u_1
inst✝ : MulAction G X
a b : X
h : ¬Disjoint (orbit G a) (orbit G b)
⊢ orbit G a = orbit G b ∨ Disjoint (orbit G a) (orbit G b) | case inr.h
G : Type u_2
inst✝¹ : Group G
X : Type u_1
inst✝ : MulAction G X
a b : X
h : ¬Disjoint (orbit G a) (orbit G b)
⊢ orbit G a = orbit G b | Please generate a tactic in lean4 to solve the state.
STATE:
case inr
G : Type u_2
inst✝¹ : Group G
X : Type u_1
inst✝ : MulAction G X
a b : X
h : ¬Disjoint (orbit G a) (orbit G b)
⊢ orbit G a = orbit G b ∨ Disjoint (orbit G a) (orbit G b)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Blocks.lean | MulAction.orbit.equal_or_disjoint | [334, 1] | [343, 20] | rw [Set.not_disjoint_iff] at h | case inr.h
G : Type u_2
inst✝¹ : Group G
X : Type u_1
inst✝ : MulAction G X
a b : X
h : ¬Disjoint (orbit G a) (orbit G b)
⊢ orbit G a = orbit G b | case inr.h
G : Type u_2
inst✝¹ : Group G
X : Type u_1
inst✝ : MulAction G X
a b : X
h : ∃ x ∈ orbit G a, x ∈ orbit G b
⊢ orbit G a = orbit G b | Please generate a tactic in lean4 to solve the state.
STATE:
case inr.h
G : Type u_2
inst✝¹ : Group G
X : Type u_1
inst✝ : MulAction G X
a b : X
h : ¬Disjoint (orbit G a) (orbit G b)
⊢ orbit G a = orbit G b
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Blocks.lean | MulAction.orbit.equal_or_disjoint | [334, 1] | [343, 20] | obtain ⟨x, hxa, hxb⟩ := h | case inr.h
G : Type u_2
inst✝¹ : Group G
X : Type u_1
inst✝ : MulAction G X
a b : X
h : ∃ x ∈ orbit G a, x ∈ orbit G b
⊢ orbit G a = orbit G b | case inr.h.intro.intro
G : Type u_2
inst✝¹ : Group G
X : Type u_1
inst✝ : MulAction G X
a b x : X
hxa : x ∈ orbit G a
hxb : x ∈ orbit G b
⊢ orbit G a = orbit G b | Please generate a tactic in lean4 to solve the state.
STATE:
case inr.h
G : Type u_2
inst✝¹ : Group G
X : Type u_1
inst✝ : MulAction G X
a b : X
h : ∃ x ∈ orbit G a, x ∈ orbit G b
⊢ orbit G a = orbit G b
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Blocks.lean | MulAction.orbit.equal_or_disjoint | [334, 1] | [343, 20] | rw [← orbit_eq_iff] at hxa hxb | case inr.h.intro.intro
G : Type u_2
inst✝¹ : Group G
X : Type u_1
inst✝ : MulAction G X
a b x : X
hxa : x ∈ orbit G a
hxb : x ∈ orbit G b
⊢ orbit G a = orbit G b | case inr.h.intro.intro
G : Type u_2
inst✝¹ : Group G
X : Type u_1
inst✝ : MulAction G X
a b x : X
hxa : orbit G x = orbit G a
hxb : orbit G x = orbit G b
⊢ orbit G a = orbit G b | Please generate a tactic in lean4 to solve the state.
STATE:
case inr.h.intro.intro
G : Type u_2
inst✝¹ : Group G
X : Type u_1
inst✝ : MulAction G X
a b x : X
hxa : x ∈ orbit G a
hxb : x ∈ orbit G b
⊢ orbit G a = orbit G b
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Blocks.lean | MulAction.orbit.equal_or_disjoint | [334, 1] | [343, 20] | rw [← hxa, ← hxb] | case inr.h.intro.intro
G : Type u_2
inst✝¹ : Group G
X : Type u_1
inst✝ : MulAction G X
a b x : X
hxa : orbit G x = orbit G a
hxb : orbit G x = orbit G b
⊢ orbit G a = orbit G b | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case inr.h.intro.intro
G : Type u_2
inst✝¹ : Group G
X : Type u_1
inst✝ : MulAction G X
a b x : X
hxa : orbit G x = orbit G a
hxb : orbit G x = orbit G b
⊢ orbit G a = orbit G b
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Blocks.lean | MulAction.orbit.equal_or_disjoint | [334, 1] | [343, 20] | apply Or.intro_right | case inl
G : Type u_2
inst✝¹ : Group G
X : Type u_1
inst✝ : MulAction G X
a b : X
h : Disjoint (orbit G a) (orbit G b)
⊢ orbit G a = orbit G b ∨ Disjoint (orbit G a) (orbit G b) | case inl.h
G : Type u_2
inst✝¹ : Group G
X : Type u_1
inst✝ : MulAction G X
a b : X
h : Disjoint (orbit G a) (orbit G b)
⊢ Disjoint (orbit G a) (orbit G b) | Please generate a tactic in lean4 to solve the state.
STATE:
case inl
G : Type u_2
inst✝¹ : Group G
X : Type u_1
inst✝ : MulAction G X
a b : X
h : Disjoint (orbit G a) (orbit G b)
⊢ orbit G a = orbit G b ∨ Disjoint (orbit G a) (orbit G b)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Blocks.lean | MulAction.orbit.equal_or_disjoint | [334, 1] | [343, 20] | exact h | case inl.h
G : Type u_2
inst✝¹ : Group G
X : Type u_1
inst✝ : MulAction G X
a b : X
h : Disjoint (orbit G a) (orbit G b)
⊢ Disjoint (orbit G a) (orbit G b) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case inl.h
G : Type u_2
inst✝¹ : Group G
X : Type u_1
inst✝ : MulAction G X
a b : X
h : Disjoint (orbit G a) (orbit G b)
⊢ Disjoint (orbit G a) (orbit G b)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Blocks.lean | MulAction.IsBlock.inter | [347, 1] | [361, 13] | rw [IsBlock.def_one] | G : Type u_2
inst✝¹ : Group G
X : Type u_1
inst✝ : MulAction G X
B₁ B₂ : Set X
h₁ : IsBlock G B₁
h₂ : IsBlock G B₂
⊢ IsBlock G (B₁ ∩ B₂) | G : Type u_2
inst✝¹ : Group G
X : Type u_1
inst✝ : MulAction G X
B₁ B₂ : Set X
h₁ : IsBlock G B₁
h₂ : IsBlock G B₂
⊢ ∀ (g : G), g • (B₁ ∩ B₂) = B₁ ∩ B₂ ∨ Disjoint (g • (B₁ ∩ B₂)) (B₁ ∩ B₂) | Please generate a tactic in lean4 to solve the state.
STATE:
G : Type u_2
inst✝¹ : Group G
X : Type u_1
inst✝ : MulAction G X
B₁ B₂ : Set X
h₁ : IsBlock G B₁
h₂ : IsBlock G B₂
⊢ IsBlock G (B₁ ∩ B₂)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Blocks.lean | MulAction.IsBlock.inter | [347, 1] | [361, 13] | intro g | G : Type u_2
inst✝¹ : Group G
X : Type u_1
inst✝ : MulAction G X
B₁ B₂ : Set X
h₁ : IsBlock G B₁
h₂ : IsBlock G B₂
⊢ ∀ (g : G), g • (B₁ ∩ B₂) = B₁ ∩ B₂ ∨ Disjoint (g • (B₁ ∩ B₂)) (B₁ ∩ B₂) | G : Type u_2
inst✝¹ : Group G
X : Type u_1
inst✝ : MulAction G X
B₁ B₂ : Set X
h₁ : IsBlock G B₁
h₂ : IsBlock G B₂
g : G
⊢ g • (B₁ ∩ B₂) = B₁ ∩ B₂ ∨ Disjoint (g • (B₁ ∩ B₂)) (B₁ ∩ B₂) | Please generate a tactic in lean4 to solve the state.
STATE:
G : Type u_2
inst✝¹ : Group G
X : Type u_1
inst✝ : MulAction G X
B₁ B₂ : Set X
h₁ : IsBlock G B₁
h₂ : IsBlock G B₂
⊢ ∀ (g : G), g • (B₁ ∩ B₂) = B₁ ∩ B₂ ∨ Disjoint (g • (B₁ ∩ B₂)) (B₁ ∩ B₂)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Blocks.lean | MulAction.IsBlock.inter | [347, 1] | [361, 13] | rw [Set.smul_set_inter] | G : Type u_2
inst✝¹ : Group G
X : Type u_1
inst✝ : MulAction G X
B₁ B₂ : Set X
h₁ : IsBlock G B₁
h₂ : IsBlock G B₂
g : G
⊢ g • (B₁ ∩ B₂) = B₁ ∩ B₂ ∨ Disjoint (g • (B₁ ∩ B₂)) (B₁ ∩ B₂) | G : Type u_2
inst✝¹ : Group G
X : Type u_1
inst✝ : MulAction G X
B₁ B₂ : Set X
h₁ : IsBlock G B₁
h₂ : IsBlock G B₂
g : G
⊢ g • B₁ ∩ g • B₂ = B₁ ∩ B₂ ∨ Disjoint (g • B₁ ∩ g • B₂) (B₁ ∩ B₂) | Please generate a tactic in lean4 to solve the state.
STATE:
G : Type u_2
inst✝¹ : Group G
X : Type u_1
inst✝ : MulAction G X
B₁ B₂ : Set X
h₁ : IsBlock G B₁
h₂ : IsBlock G B₂
g : G
⊢ g • (B₁ ∩ B₂) = B₁ ∩ B₂ ∨ Disjoint (g • (B₁ ∩ B₂)) (B₁ ∩ B₂)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Blocks.lean | MulAction.IsBlock.inter | [347, 1] | [361, 13] | cases' IsBlock.def_one.mp h₁ g with h₁ h₁ | G : Type u_2
inst✝¹ : Group G
X : Type u_1
inst✝ : MulAction G X
B₁ B₂ : Set X
h₁ : IsBlock G B₁
h₂ : IsBlock G B₂
g : G
⊢ g • B₁ ∩ g • B₂ = B₁ ∩ B₂ ∨ Disjoint (g • B₁ ∩ g • B₂) (B₁ ∩ B₂) | case inl
G : Type u_2
inst✝¹ : Group G
X : Type u_1
inst✝ : MulAction G X
B₁ B₂ : Set X
h₁✝ : IsBlock G B₁
h₂ : IsBlock G B₂
g : G
h₁ : g • B₁ = B₁
⊢ g • B₁ ∩ g • B₂ = B₁ ∩ B₂ ∨ Disjoint (g • B₁ ∩ g • B₂) (B₁ ∩ B₂)
case inr
G : Type u_2
inst✝¹ : Group G
X : Type u_1
inst✝ : MulAction G X
B₁ B₂ : Set X
h₁✝ : IsBlock G B₁
h₂ : IsBlock G B₂
g : G
h₁ : Disjoint (g • B₁) B₁
⊢ g • B₁ ∩ g • B₂ = B₁ ∩ B₂ ∨ Disjoint (g • B₁ ∩ g • B₂) (B₁ ∩ B₂) | Please generate a tactic in lean4 to solve the state.
STATE:
G : Type u_2
inst✝¹ : Group G
X : Type u_1
inst✝ : MulAction G X
B₁ B₂ : Set X
h₁ : IsBlock G B₁
h₂ : IsBlock G B₂
g : G
⊢ g • B₁ ∩ g • B₂ = B₁ ∩ B₂ ∨ Disjoint (g • B₁ ∩ g • B₂) (B₁ ∩ B₂)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Blocks.lean | MulAction.IsBlock.inter | [347, 1] | [361, 13] | cases' IsBlock.def_one.mp h₂ g with h₂ h₂ | case inl
G : Type u_2
inst✝¹ : Group G
X : Type u_1
inst✝ : MulAction G X
B₁ B₂ : Set X
h₁✝ : IsBlock G B₁
h₂ : IsBlock G B₂
g : G
h₁ : g • B₁ = B₁
⊢ g • B₁ ∩ g • B₂ = B₁ ∩ B₂ ∨ Disjoint (g • B₁ ∩ g • B₂) (B₁ ∩ B₂) | case inl.inl
G : Type u_2
inst✝¹ : Group G
X : Type u_1
inst✝ : MulAction G X
B₁ B₂ : Set X
h₁✝ : IsBlock G B₁
h₂✝ : IsBlock G B₂
g : G
h₁ : g • B₁ = B₁
h₂ : g • B₂ = B₂
⊢ g • B₁ ∩ g • B₂ = B₁ ∩ B₂ ∨ Disjoint (g • B₁ ∩ g • B₂) (B₁ ∩ B₂)
case inl.inr
G : Type u_2
inst✝¹ : Group G
X : Type u_1
inst✝ : MulAction G X
B₁ B₂ : Set X
h₁✝ : IsBlock G B₁
h₂✝ : IsBlock G B₂
g : G
h₁ : g • B₁ = B₁
h₂ : Disjoint (g • B₂) B₂
⊢ g • B₁ ∩ g • B₂ = B₁ ∩ B₂ ∨ Disjoint (g • B₁ ∩ g • B₂) (B₁ ∩ B₂) | Please generate a tactic in lean4 to solve the state.
STATE:
case inl
G : Type u_2
inst✝¹ : Group G
X : Type u_1
inst✝ : MulAction G X
B₁ B₂ : Set X
h₁✝ : IsBlock G B₁
h₂ : IsBlock G B₂
g : G
h₁ : g • B₁ = B₁
⊢ g • B₁ ∩ g • B₂ = B₁ ∩ B₂ ∨ Disjoint (g • B₁ ∩ g • B₂) (B₁ ∩ B₂)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Blocks.lean | MulAction.IsBlock.inter | [347, 1] | [361, 13] | apply Or.intro_right | case inl.inr
G : Type u_2
inst✝¹ : Group G
X : Type u_1
inst✝ : MulAction G X
B₁ B₂ : Set X
h₁✝ : IsBlock G B₁
h₂✝ : IsBlock G B₂
g : G
h₁ : g • B₁ = B₁
h₂ : Disjoint (g • B₂) B₂
⊢ g • B₁ ∩ g • B₂ = B₁ ∩ B₂ ∨ Disjoint (g • B₁ ∩ g • B₂) (B₁ ∩ B₂) | case inl.inr.h
G : Type u_2
inst✝¹ : Group G
X : Type u_1
inst✝ : MulAction G X
B₁ B₂ : Set X
h₁✝ : IsBlock G B₁
h₂✝ : IsBlock G B₂
g : G
h₁ : g • B₁ = B₁
h₂ : Disjoint (g • B₂) B₂
⊢ Disjoint (g • B₁ ∩ g • B₂) (B₁ ∩ B₂) | Please generate a tactic in lean4 to solve the state.
STATE:
case inl.inr
G : Type u_2
inst✝¹ : Group G
X : Type u_1
inst✝ : MulAction G X
B₁ B₂ : Set X
h₁✝ : IsBlock G B₁
h₂✝ : IsBlock G B₂
g : G
h₁ : g • B₁ = B₁
h₂ : Disjoint (g • B₂) B₂
⊢ g • B₁ ∩ g • B₂ = B₁ ∩ B₂ ∨ Disjoint (g • B₁ ∩ g • B₂) (B₁ ∩ B₂)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Blocks.lean | MulAction.IsBlock.inter | [347, 1] | [361, 13] | apply Disjoint.inter_left' | case inl.inr.h
G : Type u_2
inst✝¹ : Group G
X : Type u_1
inst✝ : MulAction G X
B₁ B₂ : Set X
h₁✝ : IsBlock G B₁
h₂✝ : IsBlock G B₂
g : G
h₁ : g • B₁ = B₁
h₂ : Disjoint (g • B₂) B₂
⊢ Disjoint (g • B₁ ∩ g • B₂) (B₁ ∩ B₂) | case inl.inr.h.h
G : Type u_2
inst✝¹ : Group G
X : Type u_1
inst✝ : MulAction G X
B₁ B₂ : Set X
h₁✝ : IsBlock G B₁
h₂✝ : IsBlock G B₂
g : G
h₁ : g • B₁ = B₁
h₂ : Disjoint (g • B₂) B₂
⊢ Disjoint (g • B₂) (B₁ ∩ B₂) | Please generate a tactic in lean4 to solve the state.
STATE:
case inl.inr.h
G : Type u_2
inst✝¹ : Group G
X : Type u_1
inst✝ : MulAction G X
B₁ B₂ : Set X
h₁✝ : IsBlock G B₁
h₂✝ : IsBlock G B₂
g : G
h₁ : g • B₁ = B₁
h₂ : Disjoint (g • B₂) B₂
⊢ Disjoint (g • B₁ ∩ g • B₂) (B₁ ∩ B₂)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Blocks.lean | MulAction.IsBlock.inter | [347, 1] | [361, 13] | apply Disjoint.inter_right' | case inl.inr.h.h
G : Type u_2
inst✝¹ : Group G
X : Type u_1
inst✝ : MulAction G X
B₁ B₂ : Set X
h₁✝ : IsBlock G B₁
h₂✝ : IsBlock G B₂
g : G
h₁ : g • B₁ = B₁
h₂ : Disjoint (g • B₂) B₂
⊢ Disjoint (g • B₂) (B₁ ∩ B₂) | case inl.inr.h.h.h
G : Type u_2
inst✝¹ : Group G
X : Type u_1
inst✝ : MulAction G X
B₁ B₂ : Set X
h₁✝ : IsBlock G B₁
h₂✝ : IsBlock G B₂
g : G
h₁ : g • B₁ = B₁
h₂ : Disjoint (g • B₂) B₂
⊢ Disjoint (g • B₂) B₂ | Please generate a tactic in lean4 to solve the state.
STATE:
case inl.inr.h.h
G : Type u_2
inst✝¹ : Group G
X : Type u_1
inst✝ : MulAction G X
B₁ B₂ : Set X
h₁✝ : IsBlock G B₁
h₂✝ : IsBlock G B₂
g : G
h₁ : g • B₁ = B₁
h₂ : Disjoint (g • B₂) B₂
⊢ Disjoint (g • B₂) (B₁ ∩ B₂)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Blocks.lean | MulAction.IsBlock.inter | [347, 1] | [361, 13] | exact h₂ | case inl.inr.h.h.h
G : Type u_2
inst✝¹ : Group G
X : Type u_1
inst✝ : MulAction G X
B₁ B₂ : Set X
h₁✝ : IsBlock G B₁
h₂✝ : IsBlock G B₂
g : G
h₁ : g • B₁ = B₁
h₂ : Disjoint (g • B₂) B₂
⊢ Disjoint (g • B₂) B₂ | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case inl.inr.h.h.h
G : Type u_2
inst✝¹ : Group G
X : Type u_1
inst✝ : MulAction G X
B₁ B₂ : Set X
h₁✝ : IsBlock G B₁
h₂✝ : IsBlock G B₂
g : G
h₁ : g • B₁ = B₁
h₂ : Disjoint (g • B₂) B₂
⊢ Disjoint (g • B₂) B₂
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Blocks.lean | MulAction.IsBlock.inter | [347, 1] | [361, 13] | apply Or.intro_left | case inl.inl
G : Type u_2
inst✝¹ : Group G
X : Type u_1
inst✝ : MulAction G X
B₁ B₂ : Set X
h₁✝ : IsBlock G B₁
h₂✝ : IsBlock G B₂
g : G
h₁ : g • B₁ = B₁
h₂ : g • B₂ = B₂
⊢ g • B₁ ∩ g • B₂ = B₁ ∩ B₂ ∨ Disjoint (g • B₁ ∩ g • B₂) (B₁ ∩ B₂) | case inl.inl.h
G : Type u_2
inst✝¹ : Group G
X : Type u_1
inst✝ : MulAction G X
B₁ B₂ : Set X
h₁✝ : IsBlock G B₁
h₂✝ : IsBlock G B₂
g : G
h₁ : g • B₁ = B₁
h₂ : g • B₂ = B₂
⊢ g • B₁ ∩ g • B₂ = B₁ ∩ B₂ | Please generate a tactic in lean4 to solve the state.
STATE:
case inl.inl
G : Type u_2
inst✝¹ : Group G
X : Type u_1
inst✝ : MulAction G X
B₁ B₂ : Set X
h₁✝ : IsBlock G B₁
h₂✝ : IsBlock G B₂
g : G
h₁ : g • B₁ = B₁
h₂ : g • B₂ = B₂
⊢ g • B₁ ∩ g • B₂ = B₁ ∩ B₂ ∨ Disjoint (g • B₁ ∩ g • B₂) (B₁ ∩ B₂)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Blocks.lean | MulAction.IsBlock.inter | [347, 1] | [361, 13] | rw [h₁, h₂] | case inl.inl.h
G : Type u_2
inst✝¹ : Group G
X : Type u_1
inst✝ : MulAction G X
B₁ B₂ : Set X
h₁✝ : IsBlock G B₁
h₂✝ : IsBlock G B₂
g : G
h₁ : g • B₁ = B₁
h₂ : g • B₂ = B₂
⊢ g • B₁ ∩ g • B₂ = B₁ ∩ B₂ | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case inl.inl.h
G : Type u_2
inst✝¹ : Group G
X : Type u_1
inst✝ : MulAction G X
B₁ B₂ : Set X
h₁✝ : IsBlock G B₁
h₂✝ : IsBlock G B₂
g : G
h₁ : g • B₁ = B₁
h₂ : g • B₂ = B₂
⊢ g • B₁ ∩ g • B₂ = B₁ ∩ B₂
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Blocks.lean | MulAction.IsBlock.inter | [347, 1] | [361, 13] | apply Or.intro_right | case inr
G : Type u_2
inst✝¹ : Group G
X : Type u_1
inst✝ : MulAction G X
B₁ B₂ : Set X
h₁✝ : IsBlock G B₁
h₂ : IsBlock G B₂
g : G
h₁ : Disjoint (g • B₁) B₁
⊢ g • B₁ ∩ g • B₂ = B₁ ∩ B₂ ∨ Disjoint (g • B₁ ∩ g • B₂) (B₁ ∩ B₂) | case inr.h
G : Type u_2
inst✝¹ : Group G
X : Type u_1
inst✝ : MulAction G X
B₁ B₂ : Set X
h₁✝ : IsBlock G B₁
h₂ : IsBlock G B₂
g : G
h₁ : Disjoint (g • B₁) B₁
⊢ Disjoint (g • B₁ ∩ g • B₂) (B₁ ∩ B₂) | Please generate a tactic in lean4 to solve the state.
STATE:
case inr
G : Type u_2
inst✝¹ : Group G
X : Type u_1
inst✝ : MulAction G X
B₁ B₂ : Set X
h₁✝ : IsBlock G B₁
h₂ : IsBlock G B₂
g : G
h₁ : Disjoint (g • B₁) B₁
⊢ g • B₁ ∩ g • B₂ = B₁ ∩ B₂ ∨ Disjoint (g • B₁ ∩ g • B₂) (B₁ ∩ B₂)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Blocks.lean | MulAction.IsBlock.inter | [347, 1] | [361, 13] | apply Disjoint.inter_left | case inr.h
G : Type u_2
inst✝¹ : Group G
X : Type u_1
inst✝ : MulAction G X
B₁ B₂ : Set X
h₁✝ : IsBlock G B₁
h₂ : IsBlock G B₂
g : G
h₁ : Disjoint (g • B₁) B₁
⊢ Disjoint (g • B₁ ∩ g • B₂) (B₁ ∩ B₂) | case inr.h.h
G : Type u_2
inst✝¹ : Group G
X : Type u_1
inst✝ : MulAction G X
B₁ B₂ : Set X
h₁✝ : IsBlock G B₁
h₂ : IsBlock G B₂
g : G
h₁ : Disjoint (g • B₁) B₁
⊢ Disjoint (g • B₁) (B₁ ∩ B₂) | Please generate a tactic in lean4 to solve the state.
STATE:
case inr.h
G : Type u_2
inst✝¹ : Group G
X : Type u_1
inst✝ : MulAction G X
B₁ B₂ : Set X
h₁✝ : IsBlock G B₁
h₂ : IsBlock G B₂
g : G
h₁ : Disjoint (g • B₁) B₁
⊢ Disjoint (g • B₁ ∩ g • B₂) (B₁ ∩ B₂)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Blocks.lean | MulAction.IsBlock.inter | [347, 1] | [361, 13] | apply Disjoint.inter_right | case inr.h.h
G : Type u_2
inst✝¹ : Group G
X : Type u_1
inst✝ : MulAction G X
B₁ B₂ : Set X
h₁✝ : IsBlock G B₁
h₂ : IsBlock G B₂
g : G
h₁ : Disjoint (g • B₁) B₁
⊢ Disjoint (g • B₁) (B₁ ∩ B₂) | case inr.h.h.h
G : Type u_2
inst✝¹ : Group G
X : Type u_1
inst✝ : MulAction G X
B₁ B₂ : Set X
h₁✝ : IsBlock G B₁
h₂ : IsBlock G B₂
g : G
h₁ : Disjoint (g • B₁) B₁
⊢ Disjoint (g • B₁) B₁ | Please generate a tactic in lean4 to solve the state.
STATE:
case inr.h.h
G : Type u_2
inst✝¹ : Group G
X : Type u_1
inst✝ : MulAction G X
B₁ B₂ : Set X
h₁✝ : IsBlock G B₁
h₂ : IsBlock G B₂
g : G
h₁ : Disjoint (g • B₁) B₁
⊢ Disjoint (g • B₁) (B₁ ∩ B₂)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Blocks.lean | MulAction.IsBlock.inter | [347, 1] | [361, 13] | exact h₁ | case inr.h.h.h
G : Type u_2
inst✝¹ : Group G
X : Type u_1
inst✝ : MulAction G X
B₁ B₂ : Set X
h₁✝ : IsBlock G B₁
h₂ : IsBlock G B₂
g : G
h₁ : Disjoint (g • B₁) B₁
⊢ Disjoint (g • B₁) B₁ | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case inr.h.h.h
G : Type u_2
inst✝¹ : Group G
X : Type u_1
inst✝ : MulAction G X
B₁ B₂ : Set X
h₁✝ : IsBlock G B₁
h₂ : IsBlock G B₂
g : G
h₁ : Disjoint (g • B₁) B₁
⊢ Disjoint (g • B₁) B₁
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Blocks.lean | MulAction.IsBlock.iInter | [365, 1] | [387, 29] | rw [IsBlock.def_one] | G : Type u_3
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
ι : Type u_1
B : ι → Set X
hB : ∀ (i : ι), IsBlock G (B i)
⊢ IsBlock G (⋂ i, B i) | G : Type u_3
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
ι : Type u_1
B : ι → Set X
hB : ∀ (i : ι), IsBlock G (B i)
⊢ ∀ (g : G), g • ⋂ i, B i = ⋂ i, B i ∨ Disjoint (g • ⋂ i, B i) (⋂ i, B i) | Please generate a tactic in lean4 to solve the state.
STATE:
G : Type u_3
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
ι : Type u_1
B : ι → Set X
hB : ∀ (i : ι), IsBlock G (B i)
⊢ IsBlock G (⋂ i, B i)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Blocks.lean | MulAction.IsBlock.iInter | [365, 1] | [387, 29] | cases' em (IsEmpty ι) with hι hι | G : Type u_3
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
ι : Type u_1
B : ι → Set X
hB : ∀ (i : ι), IsBlock G (B i)
⊢ ∀ (g : G), g • ⋂ i, B i = ⋂ i, B i ∨ Disjoint (g • ⋂ i, B i) (⋂ i, B i) | case inl
G : Type u_3
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
ι : Type u_1
B : ι → Set X
hB : ∀ (i : ι), IsBlock G (B i)
hι : IsEmpty ι
⊢ ∀ (g : G), g • ⋂ i, B i = ⋂ i, B i ∨ Disjoint (g • ⋂ i, B i) (⋂ i, B i)
case inr
G : Type u_3
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
ι : Type u_1
B : ι → Set X
hB : ∀ (i : ι), IsBlock G (B i)
hι : ¬IsEmpty ι
⊢ ∀ (g : G), g • ⋂ i, B i = ⋂ i, B i ∨ Disjoint (g • ⋂ i, B i) (⋂ i, B i) | Please generate a tactic in lean4 to solve the state.
STATE:
G : Type u_3
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
ι : Type u_1
B : ι → Set X
hB : ∀ (i : ι), IsBlock G (B i)
⊢ ∀ (g : G), g • ⋂ i, B i = ⋂ i, B i ∨ Disjoint (g • ⋂ i, B i) (⋂ i, B i)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Blocks.lean | MulAction.IsBlock.iInter | [365, 1] | [387, 29] | intro g | case inr
G : Type u_3
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
ι : Type u_1
B : ι → Set X
hB : ∀ (i : ι), IsBlock G (B i)
hι : ¬IsEmpty ι
⊢ ∀ (g : G), g • ⋂ i, B i = ⋂ i, B i ∨ Disjoint (g • ⋂ i, B i) (⋂ i, B i) | case inr
G : Type u_3
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
ι : Type u_1
B : ι → Set X
hB : ∀ (i : ι), IsBlock G (B i)
hι : ¬IsEmpty ι
g : G
⊢ g • ⋂ i, B i = ⋂ i, B i ∨ Disjoint (g • ⋂ i, B i) (⋂ i, B i) | Please generate a tactic in lean4 to solve the state.
STATE:
case inr
G : Type u_3
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
ι : Type u_1
B : ι → Set X
hB : ∀ (i : ι), IsBlock G (B i)
hι : ¬IsEmpty ι
⊢ ∀ (g : G), g • ⋂ i, B i = ⋂ i, B i ∨ Disjoint (g • ⋂ i, B i) (⋂ i, B i)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Blocks.lean | MulAction.IsBlock.iInter | [365, 1] | [387, 29] | rw [smul_set_iInter] | case inr
G : Type u_3
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
ι : Type u_1
B : ι → Set X
hB : ∀ (i : ι), IsBlock G (B i)
hι : ¬IsEmpty ι
g : G
⊢ g • ⋂ i, B i = ⋂ i, B i ∨ Disjoint (g • ⋂ i, B i) (⋂ i, B i) | case inr
G : Type u_3
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
ι : Type u_1
B : ι → Set X
hB : ∀ (i : ι), IsBlock G (B i)
hι : ¬IsEmpty ι
g : G
⊢ ⋂ i, g • B i = ⋂ i, B i ∨ Disjoint (⋂ i, g • B i) (⋂ i, B i) | Please generate a tactic in lean4 to solve the state.
STATE:
case inr
G : Type u_3
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
ι : Type u_1
B : ι → Set X
hB : ∀ (i : ι), IsBlock G (B i)
hι : ¬IsEmpty ι
g : G
⊢ g • ⋂ i, B i = ⋂ i, B i ∨ Disjoint (g • ⋂ i, B i) (⋂ i, B i)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Blocks.lean | MulAction.IsBlock.iInter | [365, 1] | [387, 29] | cases' em (∃ i : ι, Disjoint (g • B i) (B i)) with h h | case inr
G : Type u_3
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
ι : Type u_1
B : ι → Set X
hB : ∀ (i : ι), IsBlock G (B i)
hι : ¬IsEmpty ι
g : G
⊢ ⋂ i, g • B i = ⋂ i, B i ∨ Disjoint (⋂ i, g • B i) (⋂ i, B i) | case inr.inl
G : Type u_3
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
ι : Type u_1
B : ι → Set X
hB : ∀ (i : ι), IsBlock G (B i)
hι : ¬IsEmpty ι
g : G
h : ∃ i, Disjoint (g • B i) (B i)
⊢ ⋂ i, g • B i = ⋂ i, B i ∨ Disjoint (⋂ i, g • B i) (⋂ i, B i)
case inr.inr
G : Type u_3
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
ι : Type u_1
B : ι → Set X
hB : ∀ (i : ι), IsBlock G (B i)
hι : ¬IsEmpty ι
g : G
h : ¬∃ i, Disjoint (g • B i) (B i)
⊢ ⋂ i, g • B i = ⋂ i, B i ∨ Disjoint (⋂ i, g • B i) (⋂ i, B i) | Please generate a tactic in lean4 to solve the state.
STATE:
case inr
G : Type u_3
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
ι : Type u_1
B : ι → Set X
hB : ∀ (i : ι), IsBlock G (B i)
hι : ¬IsEmpty ι
g : G
⊢ ⋂ i, g • B i = ⋂ i, B i ∨ Disjoint (⋂ i, g • B i) (⋂ i, B i)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Blocks.lean | MulAction.IsBlock.iInter | [365, 1] | [387, 29] | simp only [not_exists] at h | case inr.inr
G : Type u_3
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
ι : Type u_1
B : ι → Set X
hB : ∀ (i : ι), IsBlock G (B i)
hι : ¬IsEmpty ι
g : G
h : ¬∃ i, Disjoint (g • B i) (B i)
⊢ ⋂ i, g • B i = ⋂ i, B i ∨ Disjoint (⋂ i, g • B i) (⋂ i, B i) | case inr.inr
G : Type u_3
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
ι : Type u_1
B : ι → Set X
hB : ∀ (i : ι), IsBlock G (B i)
hι : ¬IsEmpty ι
g : G
h : ∀ (x : ι), ¬Disjoint (g • B x) (B x)
⊢ ⋂ i, g • B i = ⋂ i, B i ∨ Disjoint (⋂ i, g • B i) (⋂ i, B i) | Please generate a tactic in lean4 to solve the state.
STATE:
case inr.inr
G : Type u_3
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
ι : Type u_1
B : ι → Set X
hB : ∀ (i : ι), IsBlock G (B i)
hι : ¬IsEmpty ι
g : G
h : ¬∃ i, Disjoint (g • B i) (B i)
⊢ ⋂ i, g • B i = ⋂ i, B i ∨ Disjoint (⋂ i, g • B i) (⋂ i, B i)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Blocks.lean | MulAction.IsBlock.iInter | [365, 1] | [387, 29] | apply Or.intro_left | case inr.inr
G : Type u_3
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
ι : Type u_1
B : ι → Set X
hB : ∀ (i : ι), IsBlock G (B i)
hι : ¬IsEmpty ι
g : G
h : ∀ (x : ι), ¬Disjoint (g • B x) (B x)
⊢ ⋂ i, g • B i = ⋂ i, B i ∨ Disjoint (⋂ i, g • B i) (⋂ i, B i) | case inr.inr.h
G : Type u_3
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
ι : Type u_1
B : ι → Set X
hB : ∀ (i : ι), IsBlock G (B i)
hι : ¬IsEmpty ι
g : G
h : ∀ (x : ι), ¬Disjoint (g • B x) (B x)
⊢ ⋂ i, g • B i = ⋂ i, B i | Please generate a tactic in lean4 to solve the state.
STATE:
case inr.inr
G : Type u_3
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
ι : Type u_1
B : ι → Set X
hB : ∀ (i : ι), IsBlock G (B i)
hι : ¬IsEmpty ι
g : G
h : ∀ (x : ι), ¬Disjoint (g • B x) (B x)
⊢ ⋂ i, g • B i = ⋂ i, B i ∨ Disjoint (⋂ i, g • B i) (⋂ i, B i)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Blocks.lean | MulAction.IsBlock.iInter | [365, 1] | [387, 29] | have : ∀ i : ι, g • B i = B i := fun i => Or.resolve_right (IsBlock.def_one.mp (hB i) g) (h i) | case inr.inr.h
G : Type u_3
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
ι : Type u_1
B : ι → Set X
hB : ∀ (i : ι), IsBlock G (B i)
hι : ¬IsEmpty ι
g : G
h : ∀ (x : ι), ¬Disjoint (g • B x) (B x)
⊢ ⋂ i, g • B i = ⋂ i, B i | case inr.inr.h
G : Type u_3
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
ι : Type u_1
B : ι → Set X
hB : ∀ (i : ι), IsBlock G (B i)
hι : ¬IsEmpty ι
g : G
h : ∀ (x : ι), ¬Disjoint (g • B x) (B x)
this : ∀ (i : ι), g • B i = B i
⊢ ⋂ i, g • B i = ⋂ i, B i | Please generate a tactic in lean4 to solve the state.
STATE:
case inr.inr.h
G : Type u_3
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
ι : Type u_1
B : ι → Set X
hB : ∀ (i : ι), IsBlock G (B i)
hι : ¬IsEmpty ι
g : G
h : ∀ (x : ι), ¬Disjoint (g • B x) (B x)
⊢ ⋂ i, g • B i = ⋂ i, B i
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Blocks.lean | MulAction.IsBlock.iInter | [365, 1] | [387, 29] | rw [Set.iInter_congr this] | case inr.inr.h
G : Type u_3
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
ι : Type u_1
B : ι → Set X
hB : ∀ (i : ι), IsBlock G (B i)
hι : ¬IsEmpty ι
g : G
h : ∀ (x : ι), ¬Disjoint (g • B x) (B x)
this : ∀ (i : ι), g • B i = B i
⊢ ⋂ i, g • B i = ⋂ i, B i | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case inr.inr.h
G : Type u_3
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
ι : Type u_1
B : ι → Set X
hB : ∀ (i : ι), IsBlock G (B i)
hι : ¬IsEmpty ι
g : G
h : ∀ (x : ι), ¬Disjoint (g • B x) (B x)
this : ∀ (i : ι), g • B i = B i
⊢ ⋂ i, g • B i = ⋂ i, B i
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Blocks.lean | MulAction.IsBlock.iInter | [365, 1] | [387, 29] | suffices (⋂ i : ι, B i) = Set.univ by
rw [this]
exact IsBlock.def_one.mp (top_IsBlock X) | case inl
G : Type u_3
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
ι : Type u_1
B : ι → Set X
hB : ∀ (i : ι), IsBlock G (B i)
hι : IsEmpty ι
⊢ ∀ (g : G), g • ⋂ i, B i = ⋂ i, B i ∨ Disjoint (g • ⋂ i, B i) (⋂ i, B i) | case inl
G : Type u_3
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
ι : Type u_1
B : ι → Set X
hB : ∀ (i : ι), IsBlock G (B i)
hι : IsEmpty ι
⊢ ⋂ i, B i = Set.univ | Please generate a tactic in lean4 to solve the state.
STATE:
case inl
G : Type u_3
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
ι : Type u_1
B : ι → Set X
hB : ∀ (i : ι), IsBlock G (B i)
hι : IsEmpty ι
⊢ ∀ (g : G), g • ⋂ i, B i = ⋂ i, B i ∨ Disjoint (g • ⋂ i, B i) (⋂ i, B i)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Blocks.lean | MulAction.IsBlock.iInter | [365, 1] | [387, 29] | simp only [Set.top_eq_univ, Set.iInter_eq_univ] | case inl
G : Type u_3
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
ι : Type u_1
B : ι → Set X
hB : ∀ (i : ι), IsBlock G (B i)
hι : IsEmpty ι
⊢ ⋂ i, B i = Set.univ | case inl
G : Type u_3
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
ι : Type u_1
B : ι → Set X
hB : ∀ (i : ι), IsBlock G (B i)
hι : IsEmpty ι
⊢ ∀ (i : ι), B i = Set.univ | Please generate a tactic in lean4 to solve the state.
STATE:
case inl
G : Type u_3
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
ι : Type u_1
B : ι → Set X
hB : ∀ (i : ι), IsBlock G (B i)
hι : IsEmpty ι
⊢ ⋂ i, B i = Set.univ
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Blocks.lean | MulAction.IsBlock.iInter | [365, 1] | [387, 29] | intro i | case inl
G : Type u_3
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
ι : Type u_1
B : ι → Set X
hB : ∀ (i : ι), IsBlock G (B i)
hι : IsEmpty ι
⊢ ∀ (i : ι), B i = Set.univ | case inl
G : Type u_3
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
ι : Type u_1
B : ι → Set X
hB : ∀ (i : ι), IsBlock G (B i)
hι : IsEmpty ι
i : ι
⊢ B i = Set.univ | Please generate a tactic in lean4 to solve the state.
STATE:
case inl
G : Type u_3
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
ι : Type u_1
B : ι → Set X
hB : ∀ (i : ι), IsBlock G (B i)
hι : IsEmpty ι
⊢ ∀ (i : ι), B i = Set.univ
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Blocks.lean | MulAction.IsBlock.iInter | [365, 1] | [387, 29] | exfalso | case inl
G : Type u_3
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
ι : Type u_1
B : ι → Set X
hB : ∀ (i : ι), IsBlock G (B i)
hι : IsEmpty ι
i : ι
⊢ B i = Set.univ | case inl
G : Type u_3
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
ι : Type u_1
B : ι → Set X
hB : ∀ (i : ι), IsBlock G (B i)
hι : IsEmpty ι
i : ι
⊢ False | Please generate a tactic in lean4 to solve the state.
STATE:
case inl
G : Type u_3
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
ι : Type u_1
B : ι → Set X
hB : ∀ (i : ι), IsBlock G (B i)
hι : IsEmpty ι
i : ι
⊢ B i = Set.univ
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Blocks.lean | MulAction.IsBlock.iInter | [365, 1] | [387, 29] | apply hι.false | case inl
G : Type u_3
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
ι : Type u_1
B : ι → Set X
hB : ∀ (i : ι), IsBlock G (B i)
hι : IsEmpty ι
i : ι
⊢ False | case inl
G : Type u_3
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
ι : Type u_1
B : ι → Set X
hB : ∀ (i : ι), IsBlock G (B i)
hι : IsEmpty ι
i : ι
⊢ ι | Please generate a tactic in lean4 to solve the state.
STATE:
case inl
G : Type u_3
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
ι : Type u_1
B : ι → Set X
hB : ∀ (i : ι), IsBlock G (B i)
hι : IsEmpty ι
i : ι
⊢ False
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Blocks.lean | MulAction.IsBlock.iInter | [365, 1] | [387, 29] | exact i | case inl
G : Type u_3
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
ι : Type u_1
B : ι → Set X
hB : ∀ (i : ι), IsBlock G (B i)
hι : IsEmpty ι
i : ι
⊢ ι | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case inl
G : Type u_3
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
ι : Type u_1
B : ι → Set X
hB : ∀ (i : ι), IsBlock G (B i)
hι : IsEmpty ι
i : ι
⊢ ι
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Blocks.lean | MulAction.IsBlock.iInter | [365, 1] | [387, 29] | rw [this] | G : Type u_3
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
ι : Type u_1
B : ι → Set X
hB : ∀ (i : ι), IsBlock G (B i)
hι : IsEmpty ι
this : ⋂ i, B i = Set.univ
⊢ ∀ (g : G), g • ⋂ i, B i = ⋂ i, B i ∨ Disjoint (g • ⋂ i, B i) (⋂ i, B i) | G : Type u_3
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
ι : Type u_1
B : ι → Set X
hB : ∀ (i : ι), IsBlock G (B i)
hι : IsEmpty ι
this : ⋂ i, B i = Set.univ
⊢ ∀ (g : G), g • Set.univ = Set.univ ∨ Disjoint (g • Set.univ) Set.univ | Please generate a tactic in lean4 to solve the state.
STATE:
G : Type u_3
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
ι : Type u_1
B : ι → Set X
hB : ∀ (i : ι), IsBlock G (B i)
hι : IsEmpty ι
this : ⋂ i, B i = Set.univ
⊢ ∀ (g : G), g • ⋂ i, B i = ⋂ i, B i ∨ Disjoint (g • ⋂ i, B i) (⋂ i, B i)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Blocks.lean | MulAction.IsBlock.iInter | [365, 1] | [387, 29] | exact IsBlock.def_one.mp (top_IsBlock X) | G : Type u_3
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
ι : Type u_1
B : ι → Set X
hB : ∀ (i : ι), IsBlock G (B i)
hι : IsEmpty ι
this : ⋂ i, B i = Set.univ
⊢ ∀ (g : G), g • Set.univ = Set.univ ∨ Disjoint (g • Set.univ) Set.univ | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
G : Type u_3
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
ι : Type u_1
B : ι → Set X
hB : ∀ (i : ι), IsBlock G (B i)
hι : IsEmpty ι
this : ⋂ i, B i = Set.univ
⊢ ∀ (g : G), g • Set.univ = Set.univ ∨ Disjoint (g • Set.univ) Set.univ
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Blocks.lean | MulAction.IsBlock.iInter | [365, 1] | [387, 29] | obtain ⟨j, hj⟩ := h | case inr.inl
G : Type u_3
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
ι : Type u_1
B : ι → Set X
hB : ∀ (i : ι), IsBlock G (B i)
hι : ¬IsEmpty ι
g : G
h : ∃ i, Disjoint (g • B i) (B i)
⊢ ⋂ i, g • B i = ⋂ i, B i ∨ Disjoint (⋂ i, g • B i) (⋂ i, B i) | case inr.inl.intro
G : Type u_3
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
ι : Type u_1
B : ι → Set X
hB : ∀ (i : ι), IsBlock G (B i)
hι : ¬IsEmpty ι
g : G
j : ι
hj : Disjoint (g • B j) (B j)
⊢ ⋂ i, g • B i = ⋂ i, B i ∨ Disjoint (⋂ i, g • B i) (⋂ i, B i) | Please generate a tactic in lean4 to solve the state.
STATE:
case inr.inl
G : Type u_3
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
ι : Type u_1
B : ι → Set X
hB : ∀ (i : ι), IsBlock G (B i)
hι : ¬IsEmpty ι
g : G
h : ∃ i, Disjoint (g • B i) (B i)
⊢ ⋂ i, g • B i = ⋂ i, B i ∨ Disjoint (⋂ i, g • B i) (⋂ i, B i)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Blocks.lean | MulAction.IsBlock.iInter | [365, 1] | [387, 29] | apply Or.intro_right | case inr.inl.intro
G : Type u_3
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
ι : Type u_1
B : ι → Set X
hB : ∀ (i : ι), IsBlock G (B i)
hι : ¬IsEmpty ι
g : G
j : ι
hj : Disjoint (g • B j) (B j)
⊢ ⋂ i, g • B i = ⋂ i, B i ∨ Disjoint (⋂ i, g • B i) (⋂ i, B i) | case inr.inl.intro.h
G : Type u_3
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
ι : Type u_1
B : ι → Set X
hB : ∀ (i : ι), IsBlock G (B i)
hι : ¬IsEmpty ι
g : G
j : ι
hj : Disjoint (g • B j) (B j)
⊢ Disjoint (⋂ i, g • B i) (⋂ i, B i) | Please generate a tactic in lean4 to solve the state.
STATE:
case inr.inl.intro
G : Type u_3
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
ι : Type u_1
B : ι → Set X
hB : ∀ (i : ι), IsBlock G (B i)
hι : ¬IsEmpty ι
g : G
j : ι
hj : Disjoint (g • B j) (B j)
⊢ ⋂ i, g • B i = ⋂ i, B i ∨ Disjoint (⋂ i, g • B i) (⋂ i, B i)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Blocks.lean | MulAction.IsBlock.iInter | [365, 1] | [387, 29] | refine' Disjoint.mono _ _ hj | case inr.inl.intro.h
G : Type u_3
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
ι : Type u_1
B : ι → Set X
hB : ∀ (i : ι), IsBlock G (B i)
hι : ¬IsEmpty ι
g : G
j : ι
hj : Disjoint (g • B j) (B j)
⊢ Disjoint (⋂ i, g • B i) (⋂ i, B i) | case inr.inl.intro.h.refine'_1
G : Type u_3
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
ι : Type u_1
B : ι → Set X
hB : ∀ (i : ι), IsBlock G (B i)
hι : ¬IsEmpty ι
g : G
j : ι
hj : Disjoint (g • B j) (B j)
⊢ ⋂ i, g • B i ≤ g • B j
case inr.inl.intro.h.refine'_2
G : Type u_3
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
ι : Type u_1
B : ι → Set X
hB : ∀ (i : ι), IsBlock G (B i)
hι : ¬IsEmpty ι
g : G
j : ι
hj : Disjoint (g • B j) (B j)
⊢ ⋂ i, B i ≤ B j | Please generate a tactic in lean4 to solve the state.
STATE:
case inr.inl.intro.h
G : Type u_3
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
ι : Type u_1
B : ι → Set X
hB : ∀ (i : ι), IsBlock G (B i)
hι : ¬IsEmpty ι
g : G
j : ι
hj : Disjoint (g • B j) (B j)
⊢ Disjoint (⋂ i, g • B i) (⋂ i, B i)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Blocks.lean | MulAction.IsBlock.iInter | [365, 1] | [387, 29] | apply Set.iInter_subset | case inr.inl.intro.h.refine'_1
G : Type u_3
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
ι : Type u_1
B : ι → Set X
hB : ∀ (i : ι), IsBlock G (B i)
hι : ¬IsEmpty ι
g : G
j : ι
hj : Disjoint (g • B j) (B j)
⊢ ⋂ i, g • B i ≤ g • B j
case inr.inl.intro.h.refine'_2
G : Type u_3
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
ι : Type u_1
B : ι → Set X
hB : ∀ (i : ι), IsBlock G (B i)
hι : ¬IsEmpty ι
g : G
j : ι
hj : Disjoint (g • B j) (B j)
⊢ ⋂ i, B i ≤ B j | case inr.inl.intro.h.refine'_2
G : Type u_3
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
ι : Type u_1
B : ι → Set X
hB : ∀ (i : ι), IsBlock G (B i)
hι : ¬IsEmpty ι
g : G
j : ι
hj : Disjoint (g • B j) (B j)
⊢ ⋂ i, B i ≤ B j | Please generate a tactic in lean4 to solve the state.
STATE:
case inr.inl.intro.h.refine'_1
G : Type u_3
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
ι : Type u_1
B : ι → Set X
hB : ∀ (i : ι), IsBlock G (B i)
hι : ¬IsEmpty ι
g : G
j : ι
hj : Disjoint (g • B j) (B j)
⊢ ⋂ i, g • B i ≤ g • B j
case inr.inl.intro.h.refine'_2
G : Type u_3
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
ι : Type u_1
B : ι → Set X
hB : ∀ (i : ι), IsBlock G (B i)
hι : ¬IsEmpty ι
g : G
j : ι
hj : Disjoint (g • B j) (B j)
⊢ ⋂ i, B i ≤ B j
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Blocks.lean | MulAction.IsBlock.iInter | [365, 1] | [387, 29] | apply Set.iInter_subset | case inr.inl.intro.h.refine'_2
G : Type u_3
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
ι : Type u_1
B : ι → Set X
hB : ∀ (i : ι), IsBlock G (B i)
hι : ¬IsEmpty ι
g : G
j : ι
hj : Disjoint (g • B j) (B j)
⊢ ⋂ i, B i ≤ B j | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case inr.inl.intro.h.refine'_2
G : Type u_3
inst✝¹ : Group G
X : Type u_2
inst✝ : MulAction G X
ι : Type u_1
B : ι → Set X
hB : ∀ (i : ι), IsBlock G (B i)
hι : ¬IsEmpty ι
g : G
j : ι
hj : Disjoint (g • B j) (B j)
⊢ ⋂ i, B i ≤ B j
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Blocks.lean | MulAction.IsBlock.of_subgroup_of_conjugate | [390, 1] | [408, 35] | rw [IsBlock.def_one] | G : Type u_2
inst✝¹ : Group G
X : Type u_1
inst✝ : MulAction G X
B : Set X
H : Subgroup G
hB : IsBlock (↥H) B
g : G
⊢ IsBlock (↥(Subgroup.map (MulEquiv.toMonoidHom (MulAut.conj g)) H)) (g • B) | G : Type u_2
inst✝¹ : Group G
X : Type u_1
inst✝ : MulAction G X
B : Set X
H : Subgroup G
hB : IsBlock (↥H) B
g : G
⊢ ∀ (g_1 : ↥(Subgroup.map (MulEquiv.toMonoidHom (MulAut.conj g)) H)),
g_1 • g • B = g • B ∨ Disjoint (g_1 • g • B) (g • B) | Please generate a tactic in lean4 to solve the state.
STATE:
G : Type u_2
inst✝¹ : Group G
X : Type u_1
inst✝ : MulAction G X
B : Set X
H : Subgroup G
hB : IsBlock (↥H) B
g : G
⊢ IsBlock (↥(Subgroup.map (MulEquiv.toMonoidHom (MulAut.conj g)) H)) (g • B)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Blocks.lean | MulAction.IsBlock.of_subgroup_of_conjugate | [390, 1] | [408, 35] | intro h' | G : Type u_2
inst✝¹ : Group G
X : Type u_1
inst✝ : MulAction G X
B : Set X
H : Subgroup G
hB : IsBlock (↥H) B
g : G
⊢ ∀ (g_1 : ↥(Subgroup.map (MulEquiv.toMonoidHom (MulAut.conj g)) H)),
g_1 • g • B = g • B ∨ Disjoint (g_1 • g • B) (g • B) | G : Type u_2
inst✝¹ : Group G
X : Type u_1
inst✝ : MulAction G X
B : Set X
H : Subgroup G
hB : IsBlock (↥H) B
g : G
h' : ↥(Subgroup.map (MulEquiv.toMonoidHom (MulAut.conj g)) H)
⊢ h' • g • B = g • B ∨ Disjoint (h' • g • B) (g • B) | Please generate a tactic in lean4 to solve the state.
STATE:
G : Type u_2
inst✝¹ : Group G
X : Type u_1
inst✝ : MulAction G X
B : Set X
H : Subgroup G
hB : IsBlock (↥H) B
g : G
⊢ ∀ (g_1 : ↥(Subgroup.map (MulEquiv.toMonoidHom (MulAut.conj g)) H)),
g_1 • g • B = g • B ∨ Disjoint (g_1 • g • B) (g • B)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Blocks.lean | MulAction.IsBlock.of_subgroup_of_conjugate | [390, 1] | [408, 35] | obtain ⟨h, hH, hh⟩ := Subgroup.mem_map.mp (SetLike.coe_mem h') | G : Type u_2
inst✝¹ : Group G
X : Type u_1
inst✝ : MulAction G X
B : Set X
H : Subgroup G
hB : IsBlock (↥H) B
g : G
h' : ↥(Subgroup.map (MulEquiv.toMonoidHom (MulAut.conj g)) H)
⊢ h' • g • B = g • B ∨ Disjoint (h' • g • B) (g • B) | case intro.intro
G : Type u_2
inst✝¹ : Group G
X : Type u_1
inst✝ : MulAction G X
B : Set X
H : Subgroup G
hB : IsBlock (↥H) B
g : G
h' : ↥(Subgroup.map (MulEquiv.toMonoidHom (MulAut.conj g)) H)
h : G
hH : h ∈ H
hh : (MulEquiv.toMonoidHom (MulAut.conj g)) h = ↑h'
⊢ h' • g • B = g • B ∨ Disjoint (h' • g • B) (g • B) | Please generate a tactic in lean4 to solve the state.
STATE:
G : Type u_2
inst✝¹ : Group G
X : Type u_1
inst✝ : MulAction G X
B : Set X
H : Subgroup G
hB : IsBlock (↥H) B
g : G
h' : ↥(Subgroup.map (MulEquiv.toMonoidHom (MulAut.conj g)) H)
⊢ h' • g • B = g • B ∨ Disjoint (h' • g • B) (g • B)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Blocks.lean | MulAction.IsBlock.of_subgroup_of_conjugate | [390, 1] | [408, 35] | simp only [MulEquiv.coe_toMonoidHom, MulAut.conj_apply] at hh | case intro.intro
G : Type u_2
inst✝¹ : Group G
X : Type u_1
inst✝ : MulAction G X
B : Set X
H : Subgroup G
hB : IsBlock (↥H) B
g : G
h' : ↥(Subgroup.map (MulEquiv.toMonoidHom (MulAut.conj g)) H)
h : G
hH : h ∈ H
hh : (MulEquiv.toMonoidHom (MulAut.conj g)) h = ↑h'
⊢ h' • g • B = g • B ∨ Disjoint (h' • g • B) (g • B) | case intro.intro
G : Type u_2
inst✝¹ : Group G
X : Type u_1
inst✝ : MulAction G X
B : Set X
H : Subgroup G
hB : IsBlock (↥H) B
g : G
h' : ↥(Subgroup.map (MulEquiv.toMonoidHom (MulAut.conj g)) H)
h : G
hH : h ∈ H
hh : g * h * g⁻¹ = ↑h'
⊢ h' • g • B = g • B ∨ Disjoint (h' • g • B) (g • B) | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro
G : Type u_2
inst✝¹ : Group G
X : Type u_1
inst✝ : MulAction G X
B : Set X
H : Subgroup G
hB : IsBlock (↥H) B
g : G
h' : ↥(Subgroup.map (MulEquiv.toMonoidHom (MulAut.conj g)) H)
h : G
hH : h ∈ H
hh : (MulEquiv.toMonoidHom (MulAut.conj g)) h = ↑h'
⊢ h' • g • B = g • B ∨ Disjoint (h' • g • B) (g • B)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Blocks.lean | MulAction.IsBlock.of_subgroup_of_conjugate | [390, 1] | [408, 35] | suffices (h' : G) • g • B = g • h • B by
rw [← this]; rfl | case intro.intro
G : Type u_2
inst✝¹ : Group G
X : Type u_1
inst✝ : MulAction G X
B : Set X
H : Subgroup G
hB : IsBlock (↥H) B
g : G
h' : ↥(Subgroup.map (MulEquiv.toMonoidHom (MulAut.conj g)) H)
h : G
hH : h ∈ H
hh : g * h * g⁻¹ = ↑h'
⊢ h' • g • B = g • h • B | case intro.intro
G : Type u_2
inst✝¹ : Group G
X : Type u_1
inst✝ : MulAction G X
B : Set X
H : Subgroup G
hB : IsBlock (↥H) B
g : G
h' : ↥(Subgroup.map (MulEquiv.toMonoidHom (MulAut.conj g)) H)
h : G
hH : h ∈ H
hh : g * h * g⁻¹ = ↑h'
⊢ ↑h' • g • B = g • h • B | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro
G : Type u_2
inst✝¹ : Group G
X : Type u_1
inst✝ : MulAction G X
B : Set X
H : Subgroup G
hB : IsBlock (↥H) B
g : G
h' : ↥(Subgroup.map (MulEquiv.toMonoidHom (MulAut.conj g)) H)
h : G
hH : h ∈ H
hh : g * h * g⁻¹ = ↑h'
⊢ h' • g • B = g • h • B
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Blocks.lean | MulAction.IsBlock.of_subgroup_of_conjugate | [390, 1] | [408, 35] | rw [← hh] | case intro.intro
G : Type u_2
inst✝¹ : Group G
X : Type u_1
inst✝ : MulAction G X
B : Set X
H : Subgroup G
hB : IsBlock (↥H) B
g : G
h' : ↥(Subgroup.map (MulEquiv.toMonoidHom (MulAut.conj g)) H)
h : G
hH : h ∈ H
hh : g * h * g⁻¹ = ↑h'
⊢ ↑h' • g • B = g • h • B | case intro.intro
G : Type u_2
inst✝¹ : Group G
X : Type u_1
inst✝ : MulAction G X
B : Set X
H : Subgroup G
hB : IsBlock (↥H) B
g : G
h' : ↥(Subgroup.map (MulEquiv.toMonoidHom (MulAut.conj g)) H)
h : G
hH : h ∈ H
hh : g * h * g⁻¹ = ↑h'
⊢ (g * h * g⁻¹) • g • B = g • h • B | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro
G : Type u_2
inst✝¹ : Group G
X : Type u_1
inst✝ : MulAction G X
B : Set X
H : Subgroup G
hB : IsBlock (↥H) B
g : G
h' : ↥(Subgroup.map (MulEquiv.toMonoidHom (MulAut.conj g)) H)
h : G
hH : h ∈ H
hh : g * h * g⁻¹ = ↑h'
⊢ ↑h' • g • B = g • h • B
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Blocks.lean | MulAction.IsBlock.of_subgroup_of_conjugate | [390, 1] | [408, 35] | rw [smul_smul (g * h * g⁻¹) g B] | case intro.intro
G : Type u_2
inst✝¹ : Group G
X : Type u_1
inst✝ : MulAction G X
B : Set X
H : Subgroup G
hB : IsBlock (↥H) B
g : G
h' : ↥(Subgroup.map (MulEquiv.toMonoidHom (MulAut.conj g)) H)
h : G
hH : h ∈ H
hh : g * h * g⁻¹ = ↑h'
⊢ (g * h * g⁻¹) • g • B = g • h • B | case intro.intro
G : Type u_2
inst✝¹ : Group G
X : Type u_1
inst✝ : MulAction G X
B : Set X
H : Subgroup G
hB : IsBlock (↥H) B
g : G
h' : ↥(Subgroup.map (MulEquiv.toMonoidHom (MulAut.conj g)) H)
h : G
hH : h ∈ H
hh : g * h * g⁻¹ = ↑h'
⊢ (g * h * g⁻¹ * g) • B = g • h • B | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro
G : Type u_2
inst✝¹ : Group G
X : Type u_1
inst✝ : MulAction G X
B : Set X
H : Subgroup G
hB : IsBlock (↥H) B
g : G
h' : ↥(Subgroup.map (MulEquiv.toMonoidHom (MulAut.conj g)) H)
h : G
hH : h ∈ H
hh : g * h * g⁻¹ = ↑h'
⊢ (g * h * g⁻¹) • g • B = g • h • B
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/Blocks.lean | MulAction.IsBlock.of_subgroup_of_conjugate | [390, 1] | [408, 35] | rw [smul_smul g h B] | case intro.intro
G : Type u_2
inst✝¹ : Group G
X : Type u_1
inst✝ : MulAction G X
B : Set X
H : Subgroup G
hB : IsBlock (↥H) B
g : G
h' : ↥(Subgroup.map (MulEquiv.toMonoidHom (MulAut.conj g)) H)
h : G
hH : h ∈ H
hh : g * h * g⁻¹ = ↑h'
⊢ (g * h * g⁻¹ * g) • B = g • h • B | case intro.intro
G : Type u_2
inst✝¹ : Group G
X : Type u_1
inst✝ : MulAction G X
B : Set X
H : Subgroup G
hB : IsBlock (↥H) B
g : G
h' : ↥(Subgroup.map (MulEquiv.toMonoidHom (MulAut.conj g)) H)
h : G
hH : h ∈ H
hh : g * h * g⁻¹ = ↑h'
⊢ (g * h * g⁻¹ * g) • B = (g * h) • B | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro
G : Type u_2
inst✝¹ : Group G
X : Type u_1
inst✝ : MulAction G X
B : Set X
H : Subgroup G
hB : IsBlock (↥H) B
g : G
h' : ↥(Subgroup.map (MulEquiv.toMonoidHom (MulAut.conj g)) H)
h : G
hH : h ∈ H
hh : g * h * g⁻¹ = ↑h'
⊢ (g * h * g⁻¹ * g) • B = g • h • B
TACTIC:
|
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