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/MultipleTransitivity.lean | MulAction.exists_smul_of_last_eq | [436, 1] | [460, 14] | use g | case intro
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
x : Fin (succ n) ↪ α
hα'eq : ∀ (x y : α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
g : M
hgx : g • x (Fin.last n) = a
⊢ ∃ g x1,
Function.Embedding.trans (Fin.castLEEmb ⋯).toEmbedding (g • x) =
... | case h
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
x : Fin (succ n) ↪ α
hα'eq : ∀ (x y : α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
g : M
hgx : g • x (Fin.last n) = a
⊢ ∃ x1,
Function.Embedding.trans (Fin.castLEEmb ⋯).toEmbedding (g • x) =
... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
x : Fin (succ n) ↪ α
hα'eq : ∀ (x y : α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
g : M
hgx : g • x (Fin.last n) = a
⊢ ∃ g x1,
Funct... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/MultipleTransitivity.lean | MulAction.exists_smul_of_last_eq | [436, 1] | [460, 14] | have zgx : ∀ (i : Fin n), g • x (Fin.castSucc i) ∈ SubMulAction.ofStabilizer M a := by
rintro ⟨i, hi⟩
rw [SubMulAction.mem_ofStabilizer_iff]
rw [← hgx]
simp only [Fin.castSucc_mk, ne_eq, smul_left_cancel_iff, EmbeddingLike.apply_eq_iff_eq, Fin.mk.injEq]
exact Fin.ne_of_lt hi | case h
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
x : Fin (succ n) ↪ α
hα'eq : ∀ (x y : α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
g : M
hgx : g • x (Fin.last n) = a
⊢ ∃ x1,
Function.Embedding.trans (Fin.castLEEmb ⋯).toEmbedding (g • x) =
... | case h
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
x : Fin (succ n) ↪ α
hα'eq : ∀ (x y : α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
g : M
hgx : g • x (Fin.last n) = a
zgx : ∀ (i : Fin n), g • x (Fin.castSucc i) ∈ SubMulAction.ofStabilizer M a
⊢ ∃ x1,
... | Please generate a tactic in lean4 to solve the state.
STATE:
case h
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
x : Fin (succ n) ↪ α
hα'eq : ∀ (x y : α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
g : M
hgx : g • x (Fin.last n) = a
⊢ ∃ x1,
Function.Em... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/MultipleTransitivity.lean | MulAction.exists_smul_of_last_eq | [436, 1] | [460, 14] | use {
toFun := fun i => ⟨g • x i, (by
simp
exact zgx i)⟩
inj' := fun i j ↦ by
simp only [Fin.coe_eq_castSucc, Subtype.mk.injEq, smul_left_cancel_iff,
EmbeddingLike.apply_eq_iff_eq, Fin.castSucc_inj, imp_self] } | case h
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
x : Fin (succ n) ↪ α
hα'eq : ∀ (x y : α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
g : M
hgx : g • x (Fin.last n) = a
zgx : ∀ (i : Fin n), g • x (Fin.castSucc i) ∈ SubMulAction.ofStabilizer M a
⊢ ∃ x1,
... | case h
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
x : Fin (succ n) ↪ α
hα'eq : ∀ (x y : α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
g : M
hgx : g • x (Fin.last n) = a
zgx : ∀ (i : Fin n), g • x (Fin.castSucc i) ∈ SubMulAction.ofStabilizer M a
⊢ Functi... | Please generate a tactic in lean4 to solve the state.
STATE:
case h
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
x : Fin (succ n) ↪ α
hα'eq : ∀ (x y : α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
g : M
hgx : g • x (Fin.last n) = a
zgx : ∀ (i : Fin n), g ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/MultipleTransitivity.lean | MulAction.exists_smul_of_last_eq | [436, 1] | [460, 14] | constructor | case h
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
x : Fin (succ n) ↪ α
hα'eq : ∀ (x y : α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
g : M
hgx : g • x (Fin.last n) = a
zgx : ∀ (i : Fin n), g • x (Fin.castSucc i) ∈ SubMulAction.ofStabilizer M a
⊢ Functi... | case h.left
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
x : Fin (succ n) ↪ α
hα'eq : ∀ (x y : α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
g : M
hgx : g • x (Fin.last n) = a
zgx : ∀ (i : Fin n), g • x (Fin.castSucc i) ∈ SubMulAction.ofStabilizer M a
⊢ F... | Please generate a tactic in lean4 to solve the state.
STATE:
case h
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
x : Fin (succ n) ↪ α
hα'eq : ∀ (x y : α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
g : M
hgx : g • x (Fin.last n) = a
zgx : ∀ (i : Fin n), g ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/MultipleTransitivity.lean | MulAction.exists_smul_of_last_eq | [436, 1] | [460, 14] | rintro ⟨i, hi⟩ | M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
x : Fin (succ n) ↪ α
hα'eq : ∀ (x y : α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
g : M
hgx : g • x (Fin.last n) = a
⊢ ∀ (i : Fin n), g • x (Fin.castSucc i) ∈ SubMulAction.ofStabilizer M a | case mk
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
x : Fin (succ n) ↪ α
hα'eq : ∀ (x y : α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
g : M
hgx : g • x (Fin.last n) = a
i : ℕ
hi : i < n
⊢ g • x (Fin.castSucc { val := i, isLt := hi }) ∈ SubMulAction.ofS... | Please generate a tactic in lean4 to solve the state.
STATE:
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
x : Fin (succ n) ↪ α
hα'eq : ∀ (x y : α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
g : M
hgx : g • x (Fin.last n) = a
⊢ ∀ (i : Fin n), g • x (Fin.ca... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/MultipleTransitivity.lean | MulAction.exists_smul_of_last_eq | [436, 1] | [460, 14] | rw [SubMulAction.mem_ofStabilizer_iff] | case mk
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
x : Fin (succ n) ↪ α
hα'eq : ∀ (x y : α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
g : M
hgx : g • x (Fin.last n) = a
i : ℕ
hi : i < n
⊢ g • x (Fin.castSucc { val := i, isLt := hi }) ∈ SubMulAction.ofS... | case mk
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
x : Fin (succ n) ↪ α
hα'eq : ∀ (x y : α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
g : M
hgx : g • x (Fin.last n) = a
i : ℕ
hi : i < n
⊢ g • x (Fin.castSucc { val := i, isLt := hi }) ≠ a | Please generate a tactic in lean4 to solve the state.
STATE:
case mk
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
x : Fin (succ n) ↪ α
hα'eq : ∀ (x y : α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
g : M
hgx : g • x (Fin.last n) = a
i : ℕ
hi : i < n
⊢ g •... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/MultipleTransitivity.lean | MulAction.exists_smul_of_last_eq | [436, 1] | [460, 14] | rw [← hgx] | case mk
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
x : Fin (succ n) ↪ α
hα'eq : ∀ (x y : α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
g : M
hgx : g • x (Fin.last n) = a
i : ℕ
hi : i < n
⊢ g • x (Fin.castSucc { val := i, isLt := hi }) ≠ a | case mk
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
x : Fin (succ n) ↪ α
hα'eq : ∀ (x y : α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
g : M
hgx : g • x (Fin.last n) = a
i : ℕ
hi : i < n
⊢ g • x (Fin.castSucc { val := i, isLt := hi }) ≠ g • x (Fin.last ... | Please generate a tactic in lean4 to solve the state.
STATE:
case mk
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
x : Fin (succ n) ↪ α
hα'eq : ∀ (x y : α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
g : M
hgx : g • x (Fin.last n) = a
i : ℕ
hi : i < n
⊢ g •... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/MultipleTransitivity.lean | MulAction.exists_smul_of_last_eq | [436, 1] | [460, 14] | simp only [Fin.castSucc_mk, ne_eq, smul_left_cancel_iff, EmbeddingLike.apply_eq_iff_eq, Fin.mk.injEq] | case mk
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
x : Fin (succ n) ↪ α
hα'eq : ∀ (x y : α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
g : M
hgx : g • x (Fin.last n) = a
i : ℕ
hi : i < n
⊢ g • x (Fin.castSucc { val := i, isLt := hi }) ≠ g • x (Fin.last ... | case mk
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
x : Fin (succ n) ↪ α
hα'eq : ∀ (x y : α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
g : M
hgx : g • x (Fin.last n) = a
i : ℕ
hi : i < n
⊢ ¬{ val := i, isLt := ⋯ } = Fin.last n | Please generate a tactic in lean4 to solve the state.
STATE:
case mk
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
x : Fin (succ n) ↪ α
hα'eq : ∀ (x y : α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
g : M
hgx : g • x (Fin.last n) = a
i : ℕ
hi : i < n
⊢ g •... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/MultipleTransitivity.lean | MulAction.exists_smul_of_last_eq | [436, 1] | [460, 14] | exact Fin.ne_of_lt hi | case mk
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
x : Fin (succ n) ↪ α
hα'eq : ∀ (x y : α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
g : M
hgx : g • x (Fin.last n) = a
i : ℕ
hi : i < n
⊢ ¬{ val := i, isLt := ⋯ } = Fin.last n | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case mk
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
x : Fin (succ n) ↪ α
hα'eq : ∀ (x y : α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
g : M
hgx : g • x (Fin.last n) = a
i : ℕ
hi : i < n
⊢ ¬{ ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/MultipleTransitivity.lean | MulAction.exists_smul_of_last_eq | [436, 1] | [460, 14] | simp | M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
x : Fin (succ n) ↪ α
hα'eq : ∀ (x y : α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
g : M
hgx : g • x (Fin.last n) = a
zgx : ∀ (i : Fin n), g • x (Fin.castSucc i) ∈ SubMulAction.ofStabilizer M a
i : Fin n
⊢ g •... | M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
x : Fin (succ n) ↪ α
hα'eq : ∀ (x y : α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
g : M
hgx : g • x (Fin.last n) = a
zgx : ∀ (i : Fin n), g • x (Fin.castSucc i) ∈ SubMulAction.ofStabilizer M a
i : Fin n
⊢ g •... | Please generate a tactic in lean4 to solve the state.
STATE:
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
x : Fin (succ n) ↪ α
hα'eq : ∀ (x y : α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
g : M
hgx : g • x (Fin.last n) = a
zgx : ∀ (i : Fin n), g • x (Fi... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/MultipleTransitivity.lean | MulAction.exists_smul_of_last_eq | [436, 1] | [460, 14] | exact zgx i | M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
x : Fin (succ n) ↪ α
hα'eq : ∀ (x y : α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
g : M
hgx : g • x (Fin.last n) = a
zgx : ∀ (i : Fin n), g • x (Fin.castSucc i) ∈ SubMulAction.ofStabilizer M a
i : Fin n
⊢ g •... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
x : Fin (succ n) ↪ α
hα'eq : ∀ (x y : α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
g : M
hgx : g • x (Fin.last n) = a
zgx : ∀ (i : Fin n), g • x (Fi... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/MultipleTransitivity.lean | MulAction.exists_smul_of_last_eq | [436, 1] | [460, 14] | simp only [Fin.coe_eq_castSucc, Subtype.mk.injEq, smul_left_cancel_iff,
EmbeddingLike.apply_eq_iff_eq, Fin.castSucc_inj, imp_self] | M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
x : Fin (succ n) ↪ α
hα'eq : ∀ (x y : α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
g : M
hgx : g • x (Fin.last n) = a
zgx : ∀ (i : Fin n), g • x (Fin.castSucc i) ∈ SubMulAction.ofStabilizer M a
i j : Fin n
⊢ (... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
x : Fin (succ n) ↪ α
hα'eq : ∀ (x y : α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
g : M
hgx : g • x (Fin.last n) = a
zgx : ∀ (i : Fin n), g • x (Fi... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/MultipleTransitivity.lean | MulAction.exists_smul_of_last_eq | [436, 1] | [460, 14] | ext i | case h.left
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
x : Fin (succ n) ↪ α
hα'eq : ∀ (x y : α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
g : M
hgx : g • x (Fin.last n) = a
zgx : ∀ (i : Fin n), g • x (Fin.castSucc i) ∈ SubMulAction.ofStabilizer M a
⊢ F... | case h.left.h
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
x : Fin (succ n) ↪ α
hα'eq : ∀ (x y : α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
g : M
hgx : g • x (Fin.last n) = a
zgx : ∀ (i : Fin n), g • x (Fin.castSucc i) ∈ SubMulAction.ofStabilizer M a
i... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.left
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
x : Fin (succ n) ↪ α
hα'eq : ∀ (x y : α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
g : M
hgx : g • x (Fin.last n) = a
zgx : ∀ (i : Fin n... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/MultipleTransitivity.lean | MulAction.exists_smul_of_last_eq | [436, 1] | [460, 14] | simp | case h.left.h
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
x : Fin (succ n) ↪ α
hα'eq : ∀ (x y : α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
g : M
hgx : g • x (Fin.last n) = a
zgx : ∀ (i : Fin n), g • x (Fin.castSucc i) ∈ SubMulAction.ofStabilizer M a
i... | case h.left.h
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
x : Fin (succ n) ↪ α
hα'eq : ∀ (x y : α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
g : M
hgx : g • x (Fin.last n) = a
zgx : ∀ (i : Fin n), g • x (Fin.castSucc i) ∈ SubMulAction.ofStabilizer M a
i... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.left.h
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
x : Fin (succ n) ↪ α
hα'eq : ∀ (x y : α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
g : M
hgx : g • x (Fin.last n) = a
zgx : ∀ (i : Fin... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/MultipleTransitivity.lean | MulAction.exists_smul_of_last_eq | [436, 1] | [460, 14] | rfl | case h.left.h
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
x : Fin (succ n) ↪ α
hα'eq : ∀ (x y : α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
g : M
hgx : g • x (Fin.last n) = a
zgx : ∀ (i : Fin n), g • x (Fin.castSucc i) ∈ SubMulAction.ofStabilizer M a
i... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h.left.h
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
x : Fin (succ n) ↪ α
hα'eq : ∀ (x y : α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
g : M
hgx : g • x (Fin.last n) = a
zgx : ∀ (i : Fin... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/MultipleTransitivity.lean | MulAction.exists_smul_of_last_eq | [436, 1] | [460, 14] | exact hgx | case h.right
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
x : Fin (succ n) ↪ α
hα'eq : ∀ (x y : α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
g : M
hgx : g • x (Fin.last n) = a
zgx : ∀ (i : Fin n), g • x (Fin.castSucc i) ∈ SubMulAction.ofStabilizer M a
⊢ ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h.right
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
x : Fin (succ n) ↪ α
hα'eq : ∀ (x y : α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
g : M
hgx : g • x (Fin.last n) = a
zgx : ∀ (i : Fin ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/MultipleTransitivity.lean | MulAction.stabilizer.isMultiplyPretransitive' | [466, 1] | [558, 57] | constructor | M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
⊢ IsMultiplyPretransitive M α (succ n) ↔
∀ (a : α), IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n | case mp
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
⊢ IsMultiplyPretransitive M α (succ n) →
∀ (a : α), IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n
case mpr
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα'... | Please generate a tactic in lean4 to solve the state.
STATE:
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
⊢ IsMultiplyPretransitive M α (succ n) ↔
∀ (a : α), IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/MultipleTransitivity.lean | MulAction.stabilizer.isMultiplyPretransitive' | [466, 1] | [558, 57] | intro hn a | case mp
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
⊢ IsMultiplyPretransitive M α (succ n) →
∀ (a : α), IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n | case mp
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
hn : IsMultiplyPretransitive M α (succ n)
a : α
⊢ IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n | Please generate a tactic in lean4 to solve the state.
STATE:
case mp
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
⊢ IsMultiplyPretransitive M α (succ n) →
∀ (a : α), IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/MultipleTransitivity.lean | MulAction.stabilizer.isMultiplyPretransitive' | [466, 1] | [558, 57] | let hn_eq := hn.exists_smul_eq | case mp
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
hn : IsMultiplyPretransitive M α (succ n)
a : α
⊢ IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n | case mp
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
hn : IsMultiplyPretransitive M α (succ n)
a : α
hn_eq : ∀ (x y : Fin (succ n) ↪ α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
⊢ IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n | Please generate a tactic in lean4 to solve the state.
STATE:
case mp
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
hn : IsMultiplyPretransitive M α (succ n)
a : α
⊢ IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/MultipleTransitivity.lean | MulAction.stabilizer.isMultiplyPretransitive' | [466, 1] | [558, 57] | apply IsPretransitive.mk | case mp
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
hn : IsMultiplyPretransitive M α (succ n)
a : α
hn_eq : ∀ (x y : Fin (succ n) ↪ α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
⊢ IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n | case mp.exists_smul_eq
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
hn : IsMultiplyPretransitive M α (succ n)
a : α
hn_eq : ∀ (x y : Fin (succ n) ↪ α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
⊢ ∀ (x y : Fin n ↪ ↥(SubMulAction.ofStabilizer M a)), ∃ g, g • x = ... | Please generate a tactic in lean4 to solve the state.
STATE:
case mp
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
hn : IsMultiplyPretransitive M α (succ n)
a : α
hn_eq : ∀ (x y : Fin (succ n) ↪ α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
⊢ IsMultiplyPretransi... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/MultipleTransitivity.lean | MulAction.stabilizer.isMultiplyPretransitive' | [466, 1] | [558, 57] | intro x y | case mp.exists_smul_eq
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
hn : IsMultiplyPretransitive M α (succ n)
a : α
hn_eq : ∀ (x y : Fin (succ n) ↪ α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
⊢ ∀ (x y : Fin n ↪ ↥(SubMulAction.ofStabilizer M a)), ∃ g, g • x = ... | case mp.exists_smul_eq
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
hn : IsMultiplyPretransitive M α (succ n)
a : α
hn_eq : ∀ (x y : Fin (succ n) ↪ α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
x y : Fin n ↪ ↥(SubMulAction.ofStabilizer M a)
⊢ ∃ g, g • x = y | Please generate a tactic in lean4 to solve the state.
STATE:
case mp.exists_smul_eq
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
hn : IsMultiplyPretransitive M α (succ n)
a : α
hn_eq : ∀ (x y : Fin (succ n) ↪ α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
⊢ ∀ (x... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/MultipleTransitivity.lean | MulAction.stabilizer.isMultiplyPretransitive' | [466, 1] | [558, 57] | obtain ⟨x', hx', hx'a⟩ := exists_extends_with_last_eq M a x | case mp.exists_smul_eq
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
hn : IsMultiplyPretransitive M α (succ n)
a : α
hn_eq : ∀ (x y : Fin (succ n) ↪ α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
x y : Fin n ↪ ↥(SubMulAction.ofStabilizer M a)
⊢ ∃ g, g • x = y | case mp.exists_smul_eq.intro.intro
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
hn : IsMultiplyPretransitive M α (succ n)
a : α
hn_eq : ∀ (x y : Fin (succ n) ↪ α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
x y : Fin n ↪ ↥(SubMulAction.ofStabilizer M a)
x' : Fin... | Please generate a tactic in lean4 to solve the state.
STATE:
case mp.exists_smul_eq
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
hn : IsMultiplyPretransitive M α (succ n)
a : α
hn_eq : ∀ (x y : Fin (succ n) ↪ α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
x y : ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/MultipleTransitivity.lean | MulAction.stabilizer.isMultiplyPretransitive' | [466, 1] | [558, 57] | obtain ⟨y', hy', hy'a⟩ := exists_extends_with_last_eq M a y | case mp.exists_smul_eq.intro.intro
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
hn : IsMultiplyPretransitive M α (succ n)
a : α
hn_eq : ∀ (x y : Fin (succ n) ↪ α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
x y : Fin n ↪ ↥(SubMulAction.ofStabilizer M a)
x' : Fin... | case mp.exists_smul_eq.intro.intro.intro.intro
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
hn : IsMultiplyPretransitive M α (succ n)
a : α
hn_eq : ∀ (x y : Fin (succ n) ↪ α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
x y : Fin n ↪ ↥(SubMulAction.ofStabilizer M... | Please generate a tactic in lean4 to solve the state.
STATE:
case mp.exists_smul_eq.intro.intro
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
hn : IsMultiplyPretransitive M α (succ n)
a : α
hn_eq : ∀ (x y : Fin (succ n) ↪ α), ∃ g, g • x = y := IsPretransitive.exists_sm... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/MultipleTransitivity.lean | MulAction.stabilizer.isMultiplyPretransitive' | [466, 1] | [558, 57] | obtain ⟨g, hg'⟩ := hn_eq x' y' | case mp.exists_smul_eq.intro.intro.intro.intro
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
hn : IsMultiplyPretransitive M α (succ n)
a : α
hn_eq : ∀ (x y : Fin (succ n) ↪ α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
x y : Fin n ↪ ↥(SubMulAction.ofStabilizer M... | case mp.exists_smul_eq.intro.intro.intro.intro.intro
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
hn : IsMultiplyPretransitive M α (succ n)
a : α
hn_eq : ∀ (x y : Fin (succ n) ↪ α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
x y : Fin n ↪ ↥(SubMulAction.ofStabil... | Please generate a tactic in lean4 to solve the state.
STATE:
case mp.exists_smul_eq.intro.intro.intro.intro
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
hn : IsMultiplyPretransitive M α (succ n)
a : α
hn_eq : ∀ (x y : Fin (succ n) ↪ α), ∃ g, g • x = y := IsPretransiti... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/MultipleTransitivity.lean | MulAction.stabilizer.isMultiplyPretransitive' | [466, 1] | [558, 57] | have hg : g ∈ stabilizer M a := by
rw [mem_stabilizer_iff]
conv_lhs => rw [← hx'a]
rw [← hy'a, ← hg', smul_apply] | case mp.exists_smul_eq.intro.intro.intro.intro.intro
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
hn : IsMultiplyPretransitive M α (succ n)
a : α
hn_eq : ∀ (x y : Fin (succ n) ↪ α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
x y : Fin n ↪ ↥(SubMulAction.ofStabil... | case mp.exists_smul_eq.intro.intro.intro.intro.intro
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
hn : IsMultiplyPretransitive M α (succ n)
a : α
hn_eq : ∀ (x y : Fin (succ n) ↪ α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
x y : Fin n ↪ ↥(SubMulAction.ofStabil... | Please generate a tactic in lean4 to solve the state.
STATE:
case mp.exists_smul_eq.intro.intro.intro.intro.intro
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
hn : IsMultiplyPretransitive M α (succ n)
a : α
hn_eq : ∀ (x y : Fin (succ n) ↪ α), ∃ g, g • x = y := IsPretr... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/MultipleTransitivity.lean | MulAction.stabilizer.isMultiplyPretransitive' | [466, 1] | [558, 57] | use ⟨g, hg⟩ | case mp.exists_smul_eq.intro.intro.intro.intro.intro
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
hn : IsMultiplyPretransitive M α (succ n)
a : α
hn_eq : ∀ (x y : Fin (succ n) ↪ α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
x y : Fin n ↪ ↥(SubMulAction.ofStabil... | case h
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
hn : IsMultiplyPretransitive M α (succ n)
a : α
hn_eq : ∀ (x y : Fin (succ n) ↪ α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
x y : Fin n ↪ ↥(SubMulAction.ofStabilizer M a)
x' : Fin (succ n) ↪ α
hx' :
Functi... | Please generate a tactic in lean4 to solve the state.
STATE:
case mp.exists_smul_eq.intro.intro.intro.intro.intro
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
hn : IsMultiplyPretransitive M α (succ n)
a : α
hn_eq : ∀ (x y : Fin (succ n) ↪ α), ∃ g, g • x = y := IsPretr... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/MultipleTransitivity.lean | MulAction.stabilizer.isMultiplyPretransitive' | [466, 1] | [558, 57] | ext ⟨i, hi⟩ | case h
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
hn : IsMultiplyPretransitive M α (succ n)
a : α
hn_eq : ∀ (x y : Fin (succ n) ↪ α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
x y : Fin n ↪ ↥(SubMulAction.ofStabilizer M a)
x' : Fin (succ n) ↪ α
hx' :
Functi... | case h.h.mk.a
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
hn : IsMultiplyPretransitive M α (succ n)
a : α
hn_eq : ∀ (x y : Fin (succ n) ↪ α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
x y : Fin n ↪ ↥(SubMulAction.ofStabilizer M a)
x' : Fin (succ n) ↪ α
hx' :
... | Please generate a tactic in lean4 to solve the state.
STATE:
case h
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
hn : IsMultiplyPretransitive M α (succ n)
a : α
hn_eq : ∀ (x y : Fin (succ n) ↪ α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
x y : Fin n ↪ ↥(SubMul... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/MultipleTransitivity.lean | MulAction.stabilizer.isMultiplyPretransitive' | [466, 1] | [558, 57] | simp only [smul_apply, SubMulAction.val_smul_of_tower] | case h.h.mk.a
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
hn : IsMultiplyPretransitive M α (succ n)
a : α
hn_eq : ∀ (x y : Fin (succ n) ↪ α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
x y : Fin n ↪ ↥(SubMulAction.ofStabilizer M a)
x' : Fin (succ n) ↪ α
hx' :
... | case h.h.mk.a
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
hn : IsMultiplyPretransitive M α (succ n)
a : α
hn_eq : ∀ (x y : Fin (succ n) ↪ α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
x y : Fin n ↪ ↥(SubMulAction.ofStabilizer M a)
x' : Fin (succ n) ↪ α
hx' :
... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.h.mk.a
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
hn : IsMultiplyPretransitive M α (succ n)
a : α
hn_eq : ∀ (x y : Fin (succ n) ↪ α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
x y : Fin n ↪ ↥... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/MultipleTransitivity.lean | MulAction.stabilizer.isMultiplyPretransitive' | [466, 1] | [558, 57] | rw [← Function.Embedding.ext_iff] at hx' hy' | case h.h.mk.a
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
hn : IsMultiplyPretransitive M α (succ n)
a : α
hn_eq : ∀ (x y : Fin (succ n) ↪ α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
x y : Fin n ↪ ↥(SubMulAction.ofStabilizer M a)
x' : Fin (succ n) ↪ α
hx' :
... | case h.h.mk.a
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
hn : IsMultiplyPretransitive M α (succ n)
a : α
hn_eq : ∀ (x y : Fin (succ n) ↪ α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
x y : Fin n ↪ ↥(SubMulAction.ofStabilizer M a)
x' : Fin (succ n) ↪ α
hx' :
... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.h.mk.a
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
hn : IsMultiplyPretransitive M α (succ n)
a : α
hn_eq : ∀ (x y : Fin (succ n) ↪ α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
x y : Fin n ↪ ↥... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/MultipleTransitivity.lean | MulAction.stabilizer.isMultiplyPretransitive' | [466, 1] | [558, 57] | specialize hx' ⟨i, hi⟩ | case h.h.mk.a
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
hn : IsMultiplyPretransitive M α (succ n)
a : α
hn_eq : ∀ (x y : Fin (succ n) ↪ α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
x y : Fin n ↪ ↥(SubMulAction.ofStabilizer M a)
x' : Fin (succ n) ↪ α
hx' :
... | case h.h.mk.a
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
hn : IsMultiplyPretransitive M α (succ n)
a : α
hn_eq : ∀ (x y : Fin (succ n) ↪ α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
x y : Fin n ↪ ↥(SubMulAction.ofStabilizer M a)
x' : Fin (succ n) ↪ α
hx'a : ... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.h.mk.a
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
hn : IsMultiplyPretransitive M α (succ n)
a : α
hn_eq : ∀ (x y : Fin (succ n) ↪ α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
x y : Fin n ↪ ↥... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/MultipleTransitivity.lean | MulAction.stabilizer.isMultiplyPretransitive' | [466, 1] | [558, 57] | specialize hy' ⟨i, hi⟩ | case h.h.mk.a
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
hn : IsMultiplyPretransitive M α (succ n)
a : α
hn_eq : ∀ (x y : Fin (succ n) ↪ α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
x y : Fin n ↪ ↥(SubMulAction.ofStabilizer M a)
x' : Fin (succ n) ↪ α
hx'a : ... | case h.h.mk.a
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
hn : IsMultiplyPretransitive M α (succ n)
a : α
hn_eq : ∀ (x y : Fin (succ n) ↪ α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
x y : Fin n ↪ ↥(SubMulAction.ofStabilizer M a)
x' : Fin (succ n) ↪ α
hx'a : ... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.h.mk.a
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
hn : IsMultiplyPretransitive M α (succ n)
a : α
hn_eq : ∀ (x y : Fin (succ n) ↪ α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
x y : Fin n ↪ ↥... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/MultipleTransitivity.lean | MulAction.stabilizer.isMultiplyPretransitive' | [466, 1] | [558, 57] | simp only [trans_apply, RelEmbedding.coe_toEmbedding, Fin.castLE_mk, id.def, coeFn_mk]
at hx' hy' | case h.h.mk.a
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
hn : IsMultiplyPretransitive M α (succ n)
a : α
hn_eq : ∀ (x y : Fin (succ n) ↪ α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
x y : Fin n ↪ ↥(SubMulAction.ofStabilizer M a)
x' : Fin (succ n) ↪ α
hx'a : ... | case h.h.mk.a
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
hn : IsMultiplyPretransitive M α (succ n)
a : α
hn_eq : ∀ (x y : Fin (succ n) ↪ α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
x y : Fin n ↪ ↥(SubMulAction.ofStabilizer M a)
x' : Fin (succ n) ↪ α
hx'a : ... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.h.mk.a
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
hn : IsMultiplyPretransitive M α (succ n)
a : α
hn_eq : ∀ (x y : Fin (succ n) ↪ α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
x y : Fin n ↪ ↥... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/MultipleTransitivity.lean | MulAction.stabilizer.isMultiplyPretransitive' | [466, 1] | [558, 57] | rw [← hx', ← hy', ← hg'] | case h.h.mk.a
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
hn : IsMultiplyPretransitive M α (succ n)
a : α
hn_eq : ∀ (x y : Fin (succ n) ↪ α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
x y : Fin n ↪ ↥(SubMulAction.ofStabilizer M a)
x' : Fin (succ n) ↪ α
hx'a : ... | case h.h.mk.a
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
hn : IsMultiplyPretransitive M α (succ n)
a : α
hn_eq : ∀ (x y : Fin (succ n) ↪ α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
x y : Fin n ↪ ↥(SubMulAction.ofStabilizer M a)
x' : Fin (succ n) ↪ α
hx'a : ... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.h.mk.a
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
hn : IsMultiplyPretransitive M α (succ n)
a : α
hn_eq : ∀ (x y : Fin (succ n) ↪ α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
x y : Fin n ↪ ↥... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/MultipleTransitivity.lean | MulAction.stabilizer.isMultiplyPretransitive' | [466, 1] | [558, 57] | rfl | case h.h.mk.a
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
hn : IsMultiplyPretransitive M α (succ n)
a : α
hn_eq : ∀ (x y : Fin (succ n) ↪ α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
x y : Fin n ↪ ↥(SubMulAction.ofStabilizer M a)
x' : Fin (succ n) ↪ α
hx'a : ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h.h.mk.a
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
hn : IsMultiplyPretransitive M α (succ n)
a : α
hn_eq : ∀ (x y : Fin (succ n) ↪ α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
x y : Fin n ↪ ↥... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/MultipleTransitivity.lean | MulAction.stabilizer.isMultiplyPretransitive' | [466, 1] | [558, 57] | rw [mem_stabilizer_iff] | M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
hn : IsMultiplyPretransitive M α (succ n)
a : α
hn_eq : ∀ (x y : Fin (succ n) ↪ α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
x y : Fin n ↪ ↥(SubMulAction.ofStabilizer M a)
x' : Fin (succ n) ↪ α
hx' :
Function.Embe... | M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
hn : IsMultiplyPretransitive M α (succ n)
a : α
hn_eq : ∀ (x y : Fin (succ n) ↪ α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
x y : Fin n ↪ ↥(SubMulAction.ofStabilizer M a)
x' : Fin (succ n) ↪ α
hx' :
Function.Embe... | Please generate a tactic in lean4 to solve the state.
STATE:
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
hn : IsMultiplyPretransitive M α (succ n)
a : α
hn_eq : ∀ (x y : Fin (succ n) ↪ α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
x y : Fin n ↪ ↥(SubMulAction.... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/MultipleTransitivity.lean | MulAction.stabilizer.isMultiplyPretransitive' | [466, 1] | [558, 57] | conv_lhs => rw [← hx'a] | M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
hn : IsMultiplyPretransitive M α (succ n)
a : α
hn_eq : ∀ (x y : Fin (succ n) ↪ α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
x y : Fin n ↪ ↥(SubMulAction.ofStabilizer M a)
x' : Fin (succ n) ↪ α
hx' :
Function.Embe... | M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
hn : IsMultiplyPretransitive M α (succ n)
a : α
hn_eq : ∀ (x y : Fin (succ n) ↪ α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
x y : Fin n ↪ ↥(SubMulAction.ofStabilizer M a)
x' : Fin (succ n) ↪ α
hx' :
Function.Embe... | Please generate a tactic in lean4 to solve the state.
STATE:
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
hn : IsMultiplyPretransitive M α (succ n)
a : α
hn_eq : ∀ (x y : Fin (succ n) ↪ α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
x y : Fin n ↪ ↥(SubMulAction.... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/MultipleTransitivity.lean | MulAction.stabilizer.isMultiplyPretransitive' | [466, 1] | [558, 57] | rw [← hy'a, ← hg', smul_apply] | M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
hn : IsMultiplyPretransitive M α (succ n)
a : α
hn_eq : ∀ (x y : Fin (succ n) ↪ α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
x y : Fin n ↪ ↥(SubMulAction.ofStabilizer M a)
x' : Fin (succ n) ↪ α
hx' :
Function.Embe... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
hn : IsMultiplyPretransitive M α (succ n)
a : α
hn_eq : ∀ (x y : Fin (succ n) ↪ α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
x y : Fin n ↪ ↥(SubMulAction.... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/MultipleTransitivity.lean | MulAction.stabilizer.isMultiplyPretransitive' | [466, 1] | [558, 57] | intro hn | case mpr
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
⊢ (∀ (a : α), IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n) →
IsMultiplyPretransitive M α (succ n) | case mpr
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
hn : ∀ (a : α), IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n
⊢ IsMultiplyPretransitive M α (succ n) | Please generate a tactic in lean4 to solve the state.
STATE:
case mpr
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
⊢ (∀ (a : α), IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n) →
IsMultiplyPretransitive M α (succ n)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/MultipleTransitivity.lean | MulAction.stabilizer.isMultiplyPretransitive' | [466, 1] | [558, 57] | apply IsPretransitive.mk | case mpr
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
hn : ∀ (a : α), IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n
⊢ IsMultiplyPretransitive M α (succ n) | case mpr.exists_smul_eq
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
hn : ∀ (a : α), IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n
⊢ ∀ (x y : Fin (succ n) ↪ α), ∃ g, g • x = y | Please generate a tactic in lean4 to solve the state.
STATE:
case mpr
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
hn : ∀ (a : α), IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n
⊢ IsMultiplyPretransitive M α (succ n)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/MultipleTransitivity.lean | MulAction.stabilizer.isMultiplyPretransitive' | [466, 1] | [558, 57] | intro x | case mpr.exists_smul_eq
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
hn : ∀ (a : α), IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n
⊢ ∀ (x y : Fin (succ n) ↪ α), ∃ g, g • x = y | case mpr.exists_smul_eq
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
hn : ∀ (a : α), IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n
x : Fin (succ n) ↪ α
⊢ ∀ (y : Fin (succ n) ↪ α), ∃ g, g • x = y | Please generate a tactic in lean4 to solve the state.
STATE:
case mpr.exists_smul_eq
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
hn : ∀ (a : α), IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n
⊢ ∀ (x y : Fin (succ n) ↪ α), ∃ g, g • x ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/MultipleTransitivity.lean | MulAction.stabilizer.isMultiplyPretransitive' | [466, 1] | [558, 57] | let a := x ⟨n, lt_add_one n⟩ | case mpr.exists_smul_eq
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
hn : ∀ (a : α), IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n
x : Fin (succ n) ↪ α
⊢ ∀ (y : Fin (succ n) ↪ α), ∃ g, g • x = y | case mpr.exists_smul_eq
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
hn : ∀ (a : α), IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n
x : Fin (succ n) ↪ α
a : α := x { val := n, isLt := ⋯ }
⊢ ∀ (y : Fin (succ n) ↪ α), ∃ g, g • x = y | Please generate a tactic in lean4 to solve the state.
STATE:
case mpr.exists_smul_eq
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
hn : ∀ (a : α), IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n
x : Fin (succ n) ↪ α
⊢ ∀ (y : Fin (succ n... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/MultipleTransitivity.lean | MulAction.stabilizer.isMultiplyPretransitive' | [466, 1] | [558, 57] | obtain ⟨gx, x1, hgx, hga⟩ := exists_smul_of_last_eq M a x | case mpr.exists_smul_eq
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
hn : ∀ (a : α), IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n
x : Fin (succ n) ↪ α
a : α := x { val := n, isLt := ⋯ }
⊢ ∀ (y : Fin (succ n) ↪ α), ∃ g, g • x = y | case mpr.exists_smul_eq.intro.intro.intro
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
hn : ∀ (a : α), IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n
x : Fin (succ n) ↪ α
a : α := x { val := n, isLt := ⋯ }
gx : M
x1 : Fin n ↪ ↥(SubMul... | Please generate a tactic in lean4 to solve the state.
STATE:
case mpr.exists_smul_eq
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
hn : ∀ (a : α), IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n
x : Fin (succ n) ↪ α
a : α := x { val := ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/MultipleTransitivity.lean | MulAction.stabilizer.isMultiplyPretransitive' | [466, 1] | [558, 57] | intro y | case mpr.exists_smul_eq.intro.intro.intro
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
hn : ∀ (a : α), IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n
x : Fin (succ n) ↪ α
a : α := x { val := n, isLt := ⋯ }
gx : M
x1 : Fin n ↪ ↥(SubMul... | case mpr.exists_smul_eq.intro.intro.intro
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
hn : ∀ (a : α), IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n
x : Fin (succ n) ↪ α
a : α := x { val := n, isLt := ⋯ }
gx : M
x1 : Fin n ↪ ↥(SubMul... | Please generate a tactic in lean4 to solve the state.
STATE:
case mpr.exists_smul_eq.intro.intro.intro
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
hn : ∀ (a : α), IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n
x : Fin (succ n) ↪ α
a ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/MultipleTransitivity.lean | MulAction.stabilizer.isMultiplyPretransitive' | [466, 1] | [558, 57] | obtain ⟨gy, y1, hgy, hgb⟩ := exists_smul_of_last_eq M a y | case mpr.exists_smul_eq.intro.intro.intro
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
hn : ∀ (a : α), IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n
x : Fin (succ n) ↪ α
a : α := x { val := n, isLt := ⋯ }
gx : M
x1 : Fin n ↪ ↥(SubMul... | case mpr.exists_smul_eq.intro.intro.intro.intro.intro.intro
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
hn : ∀ (a : α), IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n
x : Fin (succ n) ↪ α
a : α := x { val := n, isLt := ⋯ }
gx : M
x1 ... | Please generate a tactic in lean4 to solve the state.
STATE:
case mpr.exists_smul_eq.intro.intro.intro
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
hn : ∀ (a : α), IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n
x : Fin (succ n) ↪ α
a ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/MultipleTransitivity.lean | MulAction.stabilizer.isMultiplyPretransitive' | [466, 1] | [558, 57] | let hna_eq := (hn a).exists_smul_eq | case mpr.exists_smul_eq.intro.intro.intro.intro.intro.intro
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
hn : ∀ (a : α), IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n
x : Fin (succ n) ↪ α
a : α := x { val := n, isLt := ⋯ }
gx : M
x1 ... | case mpr.exists_smul_eq.intro.intro.intro.intro.intro.intro
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
hn : ∀ (a : α), IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n
x : Fin (succ n) ↪ α
a : α := x { val := n, isLt := ⋯ }
gx : M
x1 ... | Please generate a tactic in lean4 to solve the state.
STATE:
case mpr.exists_smul_eq.intro.intro.intro.intro.intro.intro
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
hn : ∀ (a : α), IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n
x : F... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/MultipleTransitivity.lean | MulAction.stabilizer.isMultiplyPretransitive' | [466, 1] | [558, 57] | obtain ⟨g, hg⟩ := hna_eq x1 y1 | case mpr.exists_smul_eq.intro.intro.intro.intro.intro.intro
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
hn : ∀ (a : α), IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n
x : Fin (succ n) ↪ α
a : α := x { val := n, isLt := ⋯ }
gx : M
x1 ... | case mpr.exists_smul_eq.intro.intro.intro.intro.intro.intro.intro
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
hn : ∀ (a : α), IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n
x : Fin (succ n) ↪ α
a : α := x { val := n, isLt := ⋯ }
gx :... | Please generate a tactic in lean4 to solve the state.
STATE:
case mpr.exists_smul_eq.intro.intro.intro.intro.intro.intro
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
hn : ∀ (a : α), IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n
x : F... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/MultipleTransitivity.lean | MulAction.stabilizer.isMultiplyPretransitive' | [466, 1] | [558, 57] | use gy⁻¹ * g * gx | case mpr.exists_smul_eq.intro.intro.intro.intro.intro.intro.intro
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
hn : ∀ (a : α), IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n
x : Fin (succ n) ↪ α
a : α := x { val := n, isLt := ⋯ }
gx :... | case h
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
hn : ∀ (a : α), IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n
x : Fin (succ n) ↪ α
a : α := x { val := n, isLt := ⋯ }
gx : M
x1 : Fin n ↪ ↥(SubMulAction.ofStabilizer M a)
hgx :
Fu... | Please generate a tactic in lean4 to solve the state.
STATE:
case mpr.exists_smul_eq.intro.intro.intro.intro.intro.intro.intro
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
hn : ∀ (a : α), IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/MultipleTransitivity.lean | MulAction.stabilizer.isMultiplyPretransitive' | [466, 1] | [558, 57] | ext ⟨i, hi⟩ | case h
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
hn : ∀ (a : α), IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n
x : Fin (succ n) ↪ α
a : α := x { val := n, isLt := ⋯ }
gx : M
x1 : Fin n ↪ ↥(SubMulAction.ofStabilizer M a)
hgx :
Fu... | case h.h.mk
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
hn : ∀ (a : α), IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n
x : Fin (succ n) ↪ α
a : α := x { val := n, isLt := ⋯ }
gx : M
x1 : Fin n ↪ ↥(SubMulAction.ofStabilizer M a)
hgx :... | Please generate a tactic in lean4 to solve the state.
STATE:
case h
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
hn : ∀ (a : α), IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n
x : Fin (succ n) ↪ α
a : α := x { val := n, isLt := ⋯ }
gx... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/MultipleTransitivity.lean | MulAction.stabilizer.isMultiplyPretransitive' | [466, 1] | [558, 57] | rw [mul_smul] | case h.h.mk
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
hn : ∀ (a : α), IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n
x : Fin (succ n) ↪ α
a : α := x { val := n, isLt := ⋯ }
gx : M
x1 : Fin n ↪ ↥(SubMulAction.ofStabilizer M a)
hgx :... | case h.h.mk
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
hn : ∀ (a : α), IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n
x : Fin (succ n) ↪ α
a : α := x { val := n, isLt := ⋯ }
gx : M
x1 : Fin n ↪ ↥(SubMulAction.ofStabilizer M a)
hgx :... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.h.mk
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
hn : ∀ (a : α), IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n
x : Fin (succ n) ↪ α
a : α := x { val := n, isLt := ⋯... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/MultipleTransitivity.lean | MulAction.stabilizer.isMultiplyPretransitive' | [466, 1] | [558, 57] | simp only [smul_apply] | case h.h.mk
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
hn : ∀ (a : α), IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n
x : Fin (succ n) ↪ α
a : α := x { val := n, isLt := ⋯ }
gx : M
x1 : Fin n ↪ ↥(SubMulAction.ofStabilizer M a)
hgx :... | case h.h.mk
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
hn : ∀ (a : α), IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n
x : Fin (succ n) ↪ α
a : α := x { val := n, isLt := ⋯ }
gx : M
x1 : Fin n ↪ ↥(SubMulAction.ofStabilizer M a)
hgx :... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.h.mk
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
hn : ∀ (a : α), IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n
x : Fin (succ n) ↪ α
a : α := x { val := n, isLt := ⋯... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/MultipleTransitivity.lean | MulAction.stabilizer.isMultiplyPretransitive' | [466, 1] | [558, 57] | cases' lt_or_eq_of_le (le_of_lt_succ hi) with hi' hi' | case h.h.mk
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
hn : ∀ (a : α), IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n
x : Fin (succ n) ↪ α
a : α := x { val := n, isLt := ⋯ }
gx : M
x1 : Fin n ↪ ↥(SubMulAction.ofStabilizer M a)
hgx :... | case h.h.mk.inl
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
hn : ∀ (a : α), IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n
x : Fin (succ n) ↪ α
a : α := x { val := n, isLt := ⋯ }
gx : M
x1 : Fin n ↪ ↥(SubMulAction.ofStabilizer M a)
h... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.h.mk
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
hn : ∀ (a : α), IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n
x : Fin (succ n) ↪ α
a : α := x { val := n, isLt := ⋯... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/MultipleTransitivity.lean | MulAction.stabilizer.isMultiplyPretransitive' | [466, 1] | [558, 57] | rw [← Function.Embedding.ext_iff] at hgx hgy hg | case h.h.mk.inl
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
hn : ∀ (a : α), IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n
x : Fin (succ n) ↪ α
a : α := x { val := n, isLt := ⋯ }
gx : M
x1 : Fin n ↪ ↥(SubMulAction.ofStabilizer M a)
h... | case h.h.mk.inl
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
hn : ∀ (a : α), IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n
x : Fin (succ n) ↪ α
a : α := x { val := n, isLt := ⋯ }
gx : M
x1 : Fin n ↪ ↥(SubMulAction.ofStabilizer M a)
h... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.h.mk.inl
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
hn : ∀ (a : α), IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n
x : Fin (succ n) ↪ α
a : α := x { val := n, isLt ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/MultipleTransitivity.lean | MulAction.stabilizer.isMultiplyPretransitive' | [466, 1] | [558, 57] | specialize hgx ⟨i, hi'⟩ | case h.h.mk.inl
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
hn : ∀ (a : α), IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n
x : Fin (succ n) ↪ α
a : α := x { val := n, isLt := ⋯ }
gx : M
x1 : Fin n ↪ ↥(SubMulAction.ofStabilizer M a)
h... | case h.h.mk.inl
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
hn : ∀ (a : α), IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n
x : Fin (succ n) ↪ α
a : α := x { val := n, isLt := ⋯ }
gx : M
x1 : Fin n ↪ ↥(SubMulAction.ofStabilizer M a)
h... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.h.mk.inl
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
hn : ∀ (a : α), IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n
x : Fin (succ n) ↪ α
a : α := x { val := n, isLt ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/MultipleTransitivity.lean | MulAction.stabilizer.isMultiplyPretransitive' | [466, 1] | [558, 57] | specialize hgy ⟨i, hi'⟩ | case h.h.mk.inl
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
hn : ∀ (a : α), IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n
x : Fin (succ n) ↪ α
a : α := x { val := n, isLt := ⋯ }
gx : M
x1 : Fin n ↪ ↥(SubMulAction.ofStabilizer M a)
h... | case h.h.mk.inl
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
hn : ∀ (a : α), IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n
x : Fin (succ n) ↪ α
a : α := x { val := n, isLt := ⋯ }
gx : M
x1 : Fin n ↪ ↥(SubMulAction.ofStabilizer M a)
h... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.h.mk.inl
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
hn : ∀ (a : α), IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n
x : Fin (succ n) ↪ α
a : α := x { val := n, isLt ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/MultipleTransitivity.lean | MulAction.stabilizer.isMultiplyPretransitive' | [466, 1] | [558, 57] | specialize hg ⟨i, hi'⟩ | case h.h.mk.inl
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
hn : ∀ (a : α), IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n
x : Fin (succ n) ↪ α
a : α := x { val := n, isLt := ⋯ }
gx : M
x1 : Fin n ↪ ↥(SubMulAction.ofStabilizer M a)
h... | case h.h.mk.inl
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
hn : ∀ (a : α), IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n
x : Fin (succ n) ↪ α
a : α := x { val := n, isLt := ⋯ }
gx : M
x1 : Fin n ↪ ↥(SubMulAction.ofStabilizer M a)
h... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.h.mk.inl
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
hn : ∀ (a : α), IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n
x : Fin (succ n) ↪ α
a : α := x { val := n, isLt ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/MultipleTransitivity.lean | MulAction.stabilizer.isMultiplyPretransitive' | [466, 1] | [558, 57] | simp only [Fin.castLEEmb_toEmbedding, trans_apply, coeFn_mk, Fin.castLE_mk,
smul_apply, zero_eq, coe_subtype] at hgx hgy hg | case h.h.mk.inl
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
hn : ∀ (a : α), IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n
x : Fin (succ n) ↪ α
a : α := x { val := n, isLt := ⋯ }
gx : M
x1 : Fin n ↪ ↥(SubMulAction.ofStabilizer M a)
h... | case h.h.mk.inl
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
hn : ∀ (a : α), IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n
x : Fin (succ n) ↪ α
a : α := x { val := n, isLt := ⋯ }
gx : M
x1 : Fin n ↪ ↥(SubMulAction.ofStabilizer M a)
h... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.h.mk.inl
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
hn : ∀ (a : α), IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n
x : Fin (succ n) ↪ α
a : α := x { val := n, isLt ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/MultipleTransitivity.lean | MulAction.stabilizer.isMultiplyPretransitive' | [466, 1] | [558, 57] | rw [hgx, mul_smul, inv_smul_eq_iff, hgy, ← hg] | case h.h.mk.inl
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
hn : ∀ (a : α), IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n
x : Fin (succ n) ↪ α
a : α := x { val := n, isLt := ⋯ }
gx : M
x1 : Fin n ↪ ↥(SubMulAction.ofStabilizer M a)
h... | case h.h.mk.inl
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
hn : ∀ (a : α), IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n
x : Fin (succ n) ↪ α
a : α := x { val := n, isLt := ⋯ }
gx : M
x1 : Fin n ↪ ↥(SubMulAction.ofStabilizer M a)
h... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.h.mk.inl
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
hn : ∀ (a : α), IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n
x : Fin (succ n) ↪ α
a : α := x { val := n, isLt ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/MultipleTransitivity.lean | MulAction.stabilizer.isMultiplyPretransitive' | [466, 1] | [558, 57] | rfl | case h.h.mk.inl
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
hn : ∀ (a : α), IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n
x : Fin (succ n) ↪ α
a : α := x { val := n, isLt := ⋯ }
gx : M
x1 : Fin n ↪ ↥(SubMulAction.ofStabilizer M a)
h... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h.h.mk.inl
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
hn : ∀ (a : α), IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n
x : Fin (succ n) ↪ α
a : α := x { val := n, isLt ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/MultipleTransitivity.lean | MulAction.stabilizer.isMultiplyPretransitive' | [466, 1] | [558, 57] | simp only [hi'] | case h.h.mk.inr
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
hn : ∀ (a : α), IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n
x : Fin (succ n) ↪ α
a : α := x { val := n, isLt := ⋯ }
gx : M
x1 : Fin n ↪ ↥(SubMulAction.ofStabilizer M a)
h... | case h.h.mk.inr
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
hn : ∀ (a : α), IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n
x : Fin (succ n) ↪ α
a : α := x { val := n, isLt := ⋯ }
gx : M
x1 : Fin n ↪ ↥(SubMulAction.ofStabilizer M a)
h... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.h.mk.inr
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
hn : ∀ (a : α), IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n
x : Fin (succ n) ↪ α
a : α := x { val := n, isLt ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/MultipleTransitivity.lean | MulAction.stabilizer.isMultiplyPretransitive' | [466, 1] | [558, 57] | dsimp [Fin.last] at hga hgb | case h.h.mk.inr
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
hn : ∀ (a : α), IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n
x : Fin (succ n) ↪ α
a : α := x { val := n, isLt := ⋯ }
gx : M
x1 : Fin n ↪ ↥(SubMulAction.ofStabilizer M a)
h... | case h.h.mk.inr
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
hn : ∀ (a : α), IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n
x : Fin (succ n) ↪ α
a : α := x { val := n, isLt := ⋯ }
gx : M
x1 : Fin n ↪ ↥(SubMulAction.ofStabilizer M a)
h... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.h.mk.inr
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
hn : ∀ (a : α), IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n
x : Fin (succ n) ↪ α
a : α := x { val := n, isLt ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/MultipleTransitivity.lean | MulAction.stabilizer.isMultiplyPretransitive' | [466, 1] | [558, 57] | rw [hga, mul_smul, inv_smul_eq_iff, hgb] | case h.h.mk.inr
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
hn : ∀ (a : α), IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n
x : Fin (succ n) ↪ α
a : α := x { val := n, isLt := ⋯ }
gx : M
x1 : Fin n ↪ ↥(SubMulAction.ofStabilizer M a)
h... | case h.h.mk.inr
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
hn : ∀ (a : α), IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n
x : Fin (succ n) ↪ α
a : α := x { val := n, isLt := ⋯ }
gx : M
x1 : Fin n ↪ ↥(SubMulAction.ofStabilizer M a)
h... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.h.mk.inr
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
hn : ∀ (a : α), IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n
x : Fin (succ n) ↪ α
a : α := x { val := n, isLt ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/MultipleTransitivity.lean | MulAction.stabilizer.isMultiplyPretransitive' | [466, 1] | [558, 57] | rw [← mem_stabilizer_iff] | case h.h.mk.inr
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
hn : ∀ (a : α), IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n
x : Fin (succ n) ↪ α
a : α := x { val := n, isLt := ⋯ }
gx : M
x1 : Fin n ↪ ↥(SubMulAction.ofStabilizer M a)
h... | case h.h.mk.inr
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
hn : ∀ (a : α), IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n
x : Fin (succ n) ↪ α
a : α := x { val := n, isLt := ⋯ }
gx : M
x1 : Fin n ↪ ↥(SubMulAction.ofStabilizer M a)
h... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.h.mk.inr
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
hn : ∀ (a : α), IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n
x : Fin (succ n) ↪ α
a : α := x { val := n, isLt ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/MultipleTransitivity.lean | MulAction.stabilizer.isMultiplyPretransitive' | [466, 1] | [558, 57] | exact SetLike.coe_mem g | case h.h.mk.inr
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
hn : ∀ (a : α), IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n
x : Fin (succ n) ↪ α
a : α := x { val := n, isLt := ⋯ }
gx : M
x1 : Fin n ↪ ↥(SubMulAction.ofStabilizer M a)
h... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h.h.mk.inr
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
hn : ∀ (a : α), IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n
x : Fin (succ n) ↪ α
a : α := x { val := n, isLt ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/MultipleTransitivity.lean | MulAction.stabilizer.isMultiplyPretransitive | [564, 1] | [631, 57] | constructor | M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
⊢ IsMultiplyPretransitive M α (succ n) ↔
IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n | case mp
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
⊢ IsMultiplyPretransitive M α (succ n) →
IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n
case mpr
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : Is... | Please generate a tactic in lean4 to solve the state.
STATE:
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
⊢ IsMultiplyPretransitive M α (succ n) ↔
IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/MultipleTransitivity.lean | MulAction.stabilizer.isMultiplyPretransitive | [564, 1] | [631, 57] | intro hn | case mp
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
⊢ IsMultiplyPretransitive M α (succ n) →
IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n | case mp
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
hn : IsMultiplyPretransitive M α (succ n)
⊢ IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n | Please generate a tactic in lean4 to solve the state.
STATE:
case mp
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
⊢ IsMultiplyPretransitive M α (succ n) →
IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/MultipleTransitivity.lean | MulAction.stabilizer.isMultiplyPretransitive | [564, 1] | [631, 57] | let hn_eq := hn.exists_smul_eq | case mp
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
hn : IsMultiplyPretransitive M α (succ n)
⊢ IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n | case mp
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
hn : IsMultiplyPretransitive M α (succ n)
hn_eq : ∀ (x y : Fin (succ n) ↪ α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
⊢ IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n | Please generate a tactic in lean4 to solve the state.
STATE:
case mp
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
hn : IsMultiplyPretransitive M α (succ n)
⊢ IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/MultipleTransitivity.lean | MulAction.stabilizer.isMultiplyPretransitive | [564, 1] | [631, 57] | apply IsPretransitive.mk | case mp
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
hn : IsMultiplyPretransitive M α (succ n)
hn_eq : ∀ (x y : Fin (succ n) ↪ α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
⊢ IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n | case mp.exists_smul_eq
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
hn : IsMultiplyPretransitive M α (succ n)
hn_eq : ∀ (x y : Fin (succ n) ↪ α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
⊢ ∀ (x y : Fin n ↪ ↥(SubMulAction.ofStabilizer M a)), ∃ g, g • x = ... | Please generate a tactic in lean4 to solve the state.
STATE:
case mp
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
hn : IsMultiplyPretransitive M α (succ n)
hn_eq : ∀ (x y : Fin (succ n) ↪ α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
⊢ IsMultiplyPretransi... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/MultipleTransitivity.lean | MulAction.stabilizer.isMultiplyPretransitive | [564, 1] | [631, 57] | intro x y | case mp.exists_smul_eq
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
hn : IsMultiplyPretransitive M α (succ n)
hn_eq : ∀ (x y : Fin (succ n) ↪ α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
⊢ ∀ (x y : Fin n ↪ ↥(SubMulAction.ofStabilizer M a)), ∃ g, g • x = ... | case mp.exists_smul_eq
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
hn : IsMultiplyPretransitive M α (succ n)
hn_eq : ∀ (x y : Fin (succ n) ↪ α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
x y : Fin n ↪ ↥(SubMulAction.ofStabilizer M a)
⊢ ∃ g, g • x = y | Please generate a tactic in lean4 to solve the state.
STATE:
case mp.exists_smul_eq
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
hn : IsMultiplyPretransitive M α (succ n)
hn_eq : ∀ (x y : Fin (succ n) ↪ α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
⊢ ∀ (x... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/MultipleTransitivity.lean | MulAction.stabilizer.isMultiplyPretransitive | [564, 1] | [631, 57] | obtain ⟨x', hx', hx'a⟩ := exists_extends_with_last_eq M a x | case mp.exists_smul_eq
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
hn : IsMultiplyPretransitive M α (succ n)
hn_eq : ∀ (x y : Fin (succ n) ↪ α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
x y : Fin n ↪ ↥(SubMulAction.ofStabilizer M a)
⊢ ∃ g, g • x = y | case mp.exists_smul_eq.intro.intro
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
hn : IsMultiplyPretransitive M α (succ n)
hn_eq : ∀ (x y : Fin (succ n) ↪ α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
x y : Fin n ↪ ↥(SubMulAction.ofStabilizer M a)
x' : Fin... | Please generate a tactic in lean4 to solve the state.
STATE:
case mp.exists_smul_eq
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
hn : IsMultiplyPretransitive M α (succ n)
hn_eq : ∀ (x y : Fin (succ n) ↪ α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
x y : ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/MultipleTransitivity.lean | MulAction.stabilizer.isMultiplyPretransitive | [564, 1] | [631, 57] | obtain ⟨y', hy', hy'a⟩ := exists_extends_with_last_eq M a y | case mp.exists_smul_eq.intro.intro
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
hn : IsMultiplyPretransitive M α (succ n)
hn_eq : ∀ (x y : Fin (succ n) ↪ α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
x y : Fin n ↪ ↥(SubMulAction.ofStabilizer M a)
x' : Fin... | case mp.exists_smul_eq.intro.intro.intro.intro
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
hn : IsMultiplyPretransitive M α (succ n)
hn_eq : ∀ (x y : Fin (succ n) ↪ α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
x y : Fin n ↪ ↥(SubMulAction.ofStabilizer M... | Please generate a tactic in lean4 to solve the state.
STATE:
case mp.exists_smul_eq.intro.intro
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
hn : IsMultiplyPretransitive M α (succ n)
hn_eq : ∀ (x y : Fin (succ n) ↪ α), ∃ g, g • x = y := IsPretransitive.exists_sm... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/MultipleTransitivity.lean | MulAction.stabilizer.isMultiplyPretransitive | [564, 1] | [631, 57] | obtain ⟨g, hg'⟩ := hn_eq x' y' | case mp.exists_smul_eq.intro.intro.intro.intro
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
hn : IsMultiplyPretransitive M α (succ n)
hn_eq : ∀ (x y : Fin (succ n) ↪ α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
x y : Fin n ↪ ↥(SubMulAction.ofStabilizer M... | case mp.exists_smul_eq.intro.intro.intro.intro.intro
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
hn : IsMultiplyPretransitive M α (succ n)
hn_eq : ∀ (x y : Fin (succ n) ↪ α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
x y : Fin n ↪ ↥(SubMulAction.ofStabil... | Please generate a tactic in lean4 to solve the state.
STATE:
case mp.exists_smul_eq.intro.intro.intro.intro
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
hn : IsMultiplyPretransitive M α (succ n)
hn_eq : ∀ (x y : Fin (succ n) ↪ α), ∃ g, g • x = y := IsPretransiti... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/MultipleTransitivity.lean | MulAction.stabilizer.isMultiplyPretransitive | [564, 1] | [631, 57] | have hg : g ∈ stabilizer M a := by
rw [mem_stabilizer_iff]
conv_lhs => rw [← hx'a]
rw [← hy'a, ← hg', smul_apply] | case mp.exists_smul_eq.intro.intro.intro.intro.intro
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
hn : IsMultiplyPretransitive M α (succ n)
hn_eq : ∀ (x y : Fin (succ n) ↪ α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
x y : Fin n ↪ ↥(SubMulAction.ofStabil... | case mp.exists_smul_eq.intro.intro.intro.intro.intro
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
hn : IsMultiplyPretransitive M α (succ n)
hn_eq : ∀ (x y : Fin (succ n) ↪ α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
x y : Fin n ↪ ↥(SubMulAction.ofStabil... | Please generate a tactic in lean4 to solve the state.
STATE:
case mp.exists_smul_eq.intro.intro.intro.intro.intro
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
hn : IsMultiplyPretransitive M α (succ n)
hn_eq : ∀ (x y : Fin (succ n) ↪ α), ∃ g, g • x = y := IsPretr... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/MultipleTransitivity.lean | MulAction.stabilizer.isMultiplyPretransitive | [564, 1] | [631, 57] | use ⟨g, hg⟩ | case mp.exists_smul_eq.intro.intro.intro.intro.intro
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
hn : IsMultiplyPretransitive M α (succ n)
hn_eq : ∀ (x y : Fin (succ n) ↪ α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
x y : Fin n ↪ ↥(SubMulAction.ofStabil... | case h
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
hn : IsMultiplyPretransitive M α (succ n)
hn_eq : ∀ (x y : Fin (succ n) ↪ α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
x y : Fin n ↪ ↥(SubMulAction.ofStabilizer M a)
x' : Fin (succ n) ↪ α
hx' :
Functi... | Please generate a tactic in lean4 to solve the state.
STATE:
case mp.exists_smul_eq.intro.intro.intro.intro.intro
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
hn : IsMultiplyPretransitive M α (succ n)
hn_eq : ∀ (x y : Fin (succ n) ↪ α), ∃ g, g • x = y := IsPretr... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/MultipleTransitivity.lean | MulAction.stabilizer.isMultiplyPretransitive | [564, 1] | [631, 57] | ext ⟨i, hi⟩ | case h
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
hn : IsMultiplyPretransitive M α (succ n)
hn_eq : ∀ (x y : Fin (succ n) ↪ α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
x y : Fin n ↪ ↥(SubMulAction.ofStabilizer M a)
x' : Fin (succ n) ↪ α
hx' :
Functi... | case h.h.mk.a
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
hn : IsMultiplyPretransitive M α (succ n)
hn_eq : ∀ (x y : Fin (succ n) ↪ α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
x y : Fin n ↪ ↥(SubMulAction.ofStabilizer M a)
x' : Fin (succ n) ↪ α
hx' :
... | Please generate a tactic in lean4 to solve the state.
STATE:
case h
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
hn : IsMultiplyPretransitive M α (succ n)
hn_eq : ∀ (x y : Fin (succ n) ↪ α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
x y : Fin n ↪ ↥(SubMul... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/MultipleTransitivity.lean | MulAction.stabilizer.isMultiplyPretransitive | [564, 1] | [631, 57] | simp only [smul_apply, SubMulAction.val_smul_of_tower] | case h.h.mk.a
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
hn : IsMultiplyPretransitive M α (succ n)
hn_eq : ∀ (x y : Fin (succ n) ↪ α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
x y : Fin n ↪ ↥(SubMulAction.ofStabilizer M a)
x' : Fin (succ n) ↪ α
hx' :
... | case h.h.mk.a
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
hn : IsMultiplyPretransitive M α (succ n)
hn_eq : ∀ (x y : Fin (succ n) ↪ α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
x y : Fin n ↪ ↥(SubMulAction.ofStabilizer M a)
x' : Fin (succ n) ↪ α
hx' :
... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.h.mk.a
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
hn : IsMultiplyPretransitive M α (succ n)
hn_eq : ∀ (x y : Fin (succ n) ↪ α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
x y : Fin n ↪ ↥... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/MultipleTransitivity.lean | MulAction.stabilizer.isMultiplyPretransitive | [564, 1] | [631, 57] | rw [← Function.Embedding.ext_iff] at hx' hy' | case h.h.mk.a
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
hn : IsMultiplyPretransitive M α (succ n)
hn_eq : ∀ (x y : Fin (succ n) ↪ α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
x y : Fin n ↪ ↥(SubMulAction.ofStabilizer M a)
x' : Fin (succ n) ↪ α
hx' :
... | case h.h.mk.a
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
hn : IsMultiplyPretransitive M α (succ n)
hn_eq : ∀ (x y : Fin (succ n) ↪ α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
x y : Fin n ↪ ↥(SubMulAction.ofStabilizer M a)
x' : Fin (succ n) ↪ α
hx' :
... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.h.mk.a
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
hn : IsMultiplyPretransitive M α (succ n)
hn_eq : ∀ (x y : Fin (succ n) ↪ α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
x y : Fin n ↪ ↥... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/MultipleTransitivity.lean | MulAction.stabilizer.isMultiplyPretransitive | [564, 1] | [631, 57] | specialize hx' ⟨i, hi⟩ | case h.h.mk.a
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
hn : IsMultiplyPretransitive M α (succ n)
hn_eq : ∀ (x y : Fin (succ n) ↪ α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
x y : Fin n ↪ ↥(SubMulAction.ofStabilizer M a)
x' : Fin (succ n) ↪ α
hx' :
... | case h.h.mk.a
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
hn : IsMultiplyPretransitive M α (succ n)
hn_eq : ∀ (x y : Fin (succ n) ↪ α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
x y : Fin n ↪ ↥(SubMulAction.ofStabilizer M a)
x' : Fin (succ n) ↪ α
hx'a : ... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.h.mk.a
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
hn : IsMultiplyPretransitive M α (succ n)
hn_eq : ∀ (x y : Fin (succ n) ↪ α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
x y : Fin n ↪ ↥... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/MultipleTransitivity.lean | MulAction.stabilizer.isMultiplyPretransitive | [564, 1] | [631, 57] | specialize hy' ⟨i, hi⟩ | case h.h.mk.a
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
hn : IsMultiplyPretransitive M α (succ n)
hn_eq : ∀ (x y : Fin (succ n) ↪ α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
x y : Fin n ↪ ↥(SubMulAction.ofStabilizer M a)
x' : Fin (succ n) ↪ α
hx'a : ... | case h.h.mk.a
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
hn : IsMultiplyPretransitive M α (succ n)
hn_eq : ∀ (x y : Fin (succ n) ↪ α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
x y : Fin n ↪ ↥(SubMulAction.ofStabilizer M a)
x' : Fin (succ n) ↪ α
hx'a : ... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.h.mk.a
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
hn : IsMultiplyPretransitive M α (succ n)
hn_eq : ∀ (x y : Fin (succ n) ↪ α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
x y : Fin n ↪ ↥... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/MultipleTransitivity.lean | MulAction.stabilizer.isMultiplyPretransitive | [564, 1] | [631, 57] | simp only [trans_apply, RelEmbedding.coe_toEmbedding, Fin.castLE_mk, id.def, coeFn_mk] at hx' hy' | case h.h.mk.a
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
hn : IsMultiplyPretransitive M α (succ n)
hn_eq : ∀ (x y : Fin (succ n) ↪ α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
x y : Fin n ↪ ↥(SubMulAction.ofStabilizer M a)
x' : Fin (succ n) ↪ α
hx'a : ... | case h.h.mk.a
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
hn : IsMultiplyPretransitive M α (succ n)
hn_eq : ∀ (x y : Fin (succ n) ↪ α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
x y : Fin n ↪ ↥(SubMulAction.ofStabilizer M a)
x' : Fin (succ n) ↪ α
hx'a : ... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.h.mk.a
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
hn : IsMultiplyPretransitive M α (succ n)
hn_eq : ∀ (x y : Fin (succ n) ↪ α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
x y : Fin n ↪ ↥... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/MultipleTransitivity.lean | MulAction.stabilizer.isMultiplyPretransitive | [564, 1] | [631, 57] | rw [← hx', ← hy', ← hg'] | case h.h.mk.a
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
hn : IsMultiplyPretransitive M α (succ n)
hn_eq : ∀ (x y : Fin (succ n) ↪ α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
x y : Fin n ↪ ↥(SubMulAction.ofStabilizer M a)
x' : Fin (succ n) ↪ α
hx'a : ... | case h.h.mk.a
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
hn : IsMultiplyPretransitive M α (succ n)
hn_eq : ∀ (x y : Fin (succ n) ↪ α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
x y : Fin n ↪ ↥(SubMulAction.ofStabilizer M a)
x' : Fin (succ n) ↪ α
hx'a : ... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.h.mk.a
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
hn : IsMultiplyPretransitive M α (succ n)
hn_eq : ∀ (x y : Fin (succ n) ↪ α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
x y : Fin n ↪ ↥... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/MultipleTransitivity.lean | MulAction.stabilizer.isMultiplyPretransitive | [564, 1] | [631, 57] | rfl | case h.h.mk.a
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
hn : IsMultiplyPretransitive M α (succ n)
hn_eq : ∀ (x y : Fin (succ n) ↪ α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
x y : Fin n ↪ ↥(SubMulAction.ofStabilizer M a)
x' : Fin (succ n) ↪ α
hx'a : ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h.h.mk.a
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
hn : IsMultiplyPretransitive M α (succ n)
hn_eq : ∀ (x y : Fin (succ n) ↪ α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
x y : Fin n ↪ ↥... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/MultipleTransitivity.lean | MulAction.stabilizer.isMultiplyPretransitive | [564, 1] | [631, 57] | rw [mem_stabilizer_iff] | M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
hn : IsMultiplyPretransitive M α (succ n)
hn_eq : ∀ (x y : Fin (succ n) ↪ α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
x y : Fin n ↪ ↥(SubMulAction.ofStabilizer M a)
x' : Fin (succ n) ↪ α
hx' :
Function.Embe... | M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
hn : IsMultiplyPretransitive M α (succ n)
hn_eq : ∀ (x y : Fin (succ n) ↪ α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
x y : Fin n ↪ ↥(SubMulAction.ofStabilizer M a)
x' : Fin (succ n) ↪ α
hx' :
Function.Embe... | Please generate a tactic in lean4 to solve the state.
STATE:
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
hn : IsMultiplyPretransitive M α (succ n)
hn_eq : ∀ (x y : Fin (succ n) ↪ α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
x y : Fin n ↪ ↥(SubMulAction.... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/MultipleTransitivity.lean | MulAction.stabilizer.isMultiplyPretransitive | [564, 1] | [631, 57] | conv_lhs => rw [← hx'a] | M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
hn : IsMultiplyPretransitive M α (succ n)
hn_eq : ∀ (x y : Fin (succ n) ↪ α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
x y : Fin n ↪ ↥(SubMulAction.ofStabilizer M a)
x' : Fin (succ n) ↪ α
hx' :
Function.Embe... | M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
hn : IsMultiplyPretransitive M α (succ n)
hn_eq : ∀ (x y : Fin (succ n) ↪ α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
x y : Fin n ↪ ↥(SubMulAction.ofStabilizer M a)
x' : Fin (succ n) ↪ α
hx' :
Function.Embe... | Please generate a tactic in lean4 to solve the state.
STATE:
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
hn : IsMultiplyPretransitive M α (succ n)
hn_eq : ∀ (x y : Fin (succ n) ↪ α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
x y : Fin n ↪ ↥(SubMulAction.... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/MultipleTransitivity.lean | MulAction.stabilizer.isMultiplyPretransitive | [564, 1] | [631, 57] | rw [← hy'a, ← hg', smul_apply] | M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
hn : IsMultiplyPretransitive M α (succ n)
hn_eq : ∀ (x y : Fin (succ n) ↪ α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
x y : Fin n ↪ ↥(SubMulAction.ofStabilizer M a)
x' : Fin (succ n) ↪ α
hx' :
Function.Embe... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
hn : IsMultiplyPretransitive M α (succ n)
hn_eq : ∀ (x y : Fin (succ n) ↪ α), ∃ g, g • x = y := IsPretransitive.exists_smul_eq
x y : Fin n ↪ ↥(SubMulAction.... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/MultipleTransitivity.lean | MulAction.stabilizer.isMultiplyPretransitive | [564, 1] | [631, 57] | intro hn | case mpr
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
⊢ IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n →
IsMultiplyPretransitive M α (succ n) | case mpr
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
hn : IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n
⊢ IsMultiplyPretransitive M α (succ n) | Please generate a tactic in lean4 to solve the state.
STATE:
case mpr
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
⊢ IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n →
IsMultiplyPretransitive M α (succ n)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/MultipleTransitivity.lean | MulAction.stabilizer.isMultiplyPretransitive | [564, 1] | [631, 57] | apply IsPretransitive.mk | case mpr
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
hn : IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n
⊢ IsMultiplyPretransitive M α (succ n) | case mpr.exists_smul_eq
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
hn : IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n
⊢ ∀ (x y : Fin (succ n) ↪ α), ∃ g, g • x = y | Please generate a tactic in lean4 to solve the state.
STATE:
case mpr
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
hn : IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n
⊢ IsMultiplyPretransitive M α (succ n)
TACTIC:
|
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/MultipleTransitivity.lean | MulAction.stabilizer.isMultiplyPretransitive | [564, 1] | [631, 57] | intro x | case mpr.exists_smul_eq
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
hn : IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n
⊢ ∀ (x y : Fin (succ n) ↪ α), ∃ g, g • x = y | case mpr.exists_smul_eq
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
hn : IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n
x : Fin (succ n) ↪ α
⊢ ∀ (y : Fin (succ n) ↪ α), ∃ g, g • x = y | Please generate a tactic in lean4 to solve the state.
STATE:
case mpr.exists_smul_eq
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
hn : IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n
⊢ ∀ (x y : Fin (succ n) ↪ α), ∃ g, g • x = y
T... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/MultipleTransitivity.lean | MulAction.stabilizer.isMultiplyPretransitive | [564, 1] | [631, 57] | obtain ⟨gx, x1, hgx, hga⟩ := exists_smul_of_last_eq M a x | case mpr.exists_smul_eq
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
hn : IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n
x : Fin (succ n) ↪ α
⊢ ∀ (y : Fin (succ n) ↪ α), ∃ g, g • x = y | case mpr.exists_smul_eq.intro.intro.intro
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
hn : IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n
x : Fin (succ n) ↪ α
gx : M
x1 : Fin n ↪ ↥(SubMulAction.ofStabilizer M a)
hgx :
Functio... | Please generate a tactic in lean4 to solve the state.
STATE:
case mpr.exists_smul_eq
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
hn : IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n
x : Fin (succ n) ↪ α
⊢ ∀ (y : Fin (succ n) ↪ α... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/MultipleTransitivity.lean | MulAction.stabilizer.isMultiplyPretransitive | [564, 1] | [631, 57] | intro y | case mpr.exists_smul_eq.intro.intro.intro
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
hn : IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n
x : Fin (succ n) ↪ α
gx : M
x1 : Fin n ↪ ↥(SubMulAction.ofStabilizer M a)
hgx :
Functio... | case mpr.exists_smul_eq.intro.intro.intro
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
hn : IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n
x : Fin (succ n) ↪ α
gx : M
x1 : Fin n ↪ ↥(SubMulAction.ofStabilizer M a)
hgx :
Functio... | Please generate a tactic in lean4 to solve the state.
STATE:
case mpr.exists_smul_eq.intro.intro.intro
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
hn : IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n
x : Fin (succ n) ↪ α
gx : M
... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/MultipleTransitivity.lean | MulAction.stabilizer.isMultiplyPretransitive | [564, 1] | [631, 57] | obtain ⟨gy, y1, hgy, hgb⟩ := exists_smul_of_last_eq M a y | case mpr.exists_smul_eq.intro.intro.intro
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
hn : IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n
x : Fin (succ n) ↪ α
gx : M
x1 : Fin n ↪ ↥(SubMulAction.ofStabilizer M a)
hgx :
Functio... | case mpr.exists_smul_eq.intro.intro.intro.intro.intro.intro
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
hn : IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n
x : Fin (succ n) ↪ α
gx : M
x1 : Fin n ↪ ↥(SubMulAction.ofStabilizer M ... | Please generate a tactic in lean4 to solve the state.
STATE:
case mpr.exists_smul_eq.intro.intro.intro
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
hn : IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n
x : Fin (succ n) ↪ α
gx : M
... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/MultipleTransitivity.lean | MulAction.stabilizer.isMultiplyPretransitive | [564, 1] | [631, 57] | let hna_eq := hn.exists_smul_eq | case mpr.exists_smul_eq.intro.intro.intro.intro.intro.intro
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
hn : IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n
x : Fin (succ n) ↪ α
gx : M
x1 : Fin n ↪ ↥(SubMulAction.ofStabilizer M ... | case mpr.exists_smul_eq.intro.intro.intro.intro.intro.intro
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
hn : IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n
x : Fin (succ n) ↪ α
gx : M
x1 : Fin n ↪ ↥(SubMulAction.ofStabilizer M ... | Please generate a tactic in lean4 to solve the state.
STATE:
case mpr.exists_smul_eq.intro.intro.intro.intro.intro.intro
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
hn : IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n
x : Fin (s... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/MultipleTransitivity.lean | MulAction.stabilizer.isMultiplyPretransitive | [564, 1] | [631, 57] | obtain ⟨g, hg⟩ := hna_eq x1 y1 | case mpr.exists_smul_eq.intro.intro.intro.intro.intro.intro
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
hn : IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n
x : Fin (succ n) ↪ α
gx : M
x1 : Fin n ↪ ↥(SubMulAction.ofStabilizer M ... | case mpr.exists_smul_eq.intro.intro.intro.intro.intro.intro.intro
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
hn : IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n
x : Fin (succ n) ↪ α
gx : M
x1 : Fin n ↪ ↥(SubMulAction.ofStabili... | Please generate a tactic in lean4 to solve the state.
STATE:
case mpr.exists_smul_eq.intro.intro.intro.intro.intro.intro
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
hn : IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n
x : Fin (s... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/MultipleTransitivity.lean | MulAction.stabilizer.isMultiplyPretransitive | [564, 1] | [631, 57] | use gy⁻¹ * g * gx | case mpr.exists_smul_eq.intro.intro.intro.intro.intro.intro.intro
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
hn : IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n
x : Fin (succ n) ↪ α
gx : M
x1 : Fin n ↪ ↥(SubMulAction.ofStabili... | case h
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
hn : IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n
x : Fin (succ n) ↪ α
gx : M
x1 : Fin n ↪ ↥(SubMulAction.ofStabilizer M a)
hgx :
Function.Embedding.trans (Fin.castLEEmb ⋯)... | Please generate a tactic in lean4 to solve the state.
STATE:
case mpr.exists_smul_eq.intro.intro.intro.intro.intro.intro.intro
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
hn : IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n
x : ... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/MultipleTransitivity.lean | MulAction.stabilizer.isMultiplyPretransitive | [564, 1] | [631, 57] | ext ⟨i, hi⟩ | case h
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
hn : IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n
x : Fin (succ n) ↪ α
gx : M
x1 : Fin n ↪ ↥(SubMulAction.ofStabilizer M a)
hgx :
Function.Embedding.trans (Fin.castLEEmb ⋯)... | case h.h.mk
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
hn : IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n
x : Fin (succ n) ↪ α
gx : M
x1 : Fin n ↪ ↥(SubMulAction.ofStabilizer M a)
hgx :
Function.Embedding.trans (Fin.castLEE... | Please generate a tactic in lean4 to solve the state.
STATE:
case h
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
hn : IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n
x : Fin (succ n) ↪ α
gx : M
x1 : Fin n ↪ ↥(SubMulAction.ofStabi... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/MultipleTransitivity.lean | MulAction.stabilizer.isMultiplyPretransitive | [564, 1] | [631, 57] | rw [mul_smul] | case h.h.mk
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
hn : IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n
x : Fin (succ n) ↪ α
gx : M
x1 : Fin n ↪ ↥(SubMulAction.ofStabilizer M a)
hgx :
Function.Embedding.trans (Fin.castLEE... | case h.h.mk
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
hn : IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n
x : Fin (succ n) ↪ α
gx : M
x1 : Fin n ↪ ↥(SubMulAction.ofStabilizer M a)
hgx :
Function.Embedding.trans (Fin.castLEE... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.h.mk
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
hn : IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n
x : Fin (succ n) ↪ α
gx : M
x1 : Fin n ↪ ↥(SubMulAction.of... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/MultipleTransitivity.lean | MulAction.stabilizer.isMultiplyPretransitive | [564, 1] | [631, 57] | simp only [smul_apply] | case h.h.mk
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
hn : IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n
x : Fin (succ n) ↪ α
gx : M
x1 : Fin n ↪ ↥(SubMulAction.ofStabilizer M a)
hgx :
Function.Embedding.trans (Fin.castLEE... | case h.h.mk
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
hn : IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n
x : Fin (succ n) ↪ α
gx : M
x1 : Fin n ↪ ↥(SubMulAction.ofStabilizer M a)
hgx :
Function.Embedding.trans (Fin.castLEE... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.h.mk
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
hn : IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n
x : Fin (succ n) ↪ α
gx : M
x1 : Fin n ↪ ↥(SubMulAction.of... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/MultipleTransitivity.lean | MulAction.stabilizer.isMultiplyPretransitive | [564, 1] | [631, 57] | cases' lt_or_eq_of_le (le_of_lt_succ hi) with hi' hi' | case h.h.mk
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
hn : IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n
x : Fin (succ n) ↪ α
gx : M
x1 : Fin n ↪ ↥(SubMulAction.ofStabilizer M a)
hgx :
Function.Embedding.trans (Fin.castLEE... | case h.h.mk.inl
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
hn : IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n
x : Fin (succ n) ↪ α
gx : M
x1 : Fin n ↪ ↥(SubMulAction.ofStabilizer M a)
hgx :
Function.Embedding.trans (Fin.cas... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.h.mk
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
hn : IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n
x : Fin (succ n) ↪ α
gx : M
x1 : Fin n ↪ ↥(SubMulAction.of... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/MultipleTransitivity.lean | MulAction.stabilizer.isMultiplyPretransitive | [564, 1] | [631, 57] | rw [← Function.Embedding.ext_iff] at hgx hgy hg | case h.h.mk.inl
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
hn : IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n
x : Fin (succ n) ↪ α
gx : M
x1 : Fin n ↪ ↥(SubMulAction.ofStabilizer M a)
hgx :
Function.Embedding.trans (Fin.cas... | case h.h.mk.inl
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
hn : IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n
x : Fin (succ n) ↪ α
gx : M
x1 : Fin n ↪ ↥(SubMulAction.ofStabilizer M a)
hgx :
∀ (x_1 : Fin n),
(Function.Em... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.h.mk.inl
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
hn : IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n
x : Fin (succ n) ↪ α
gx : M
x1 : Fin n ↪ ↥(SubMulActio... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/MultipleTransitivity.lean | MulAction.stabilizer.isMultiplyPretransitive | [564, 1] | [631, 57] | specialize hgx ⟨i, hi'⟩ | case h.h.mk.inl
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
hn : IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n
x : Fin (succ n) ↪ α
gx : M
x1 : Fin n ↪ ↥(SubMulAction.ofStabilizer M a)
hgx :
∀ (x_1 : Fin n),
(Function.Em... | case h.h.mk.inl
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
hn : IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n
x : Fin (succ n) ↪ α
gx : M
x1 : Fin n ↪ ↥(SubMulAction.ofStabilizer M a)
hga : gx • x (Fin.last n) = a
y : Fin (su... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.h.mk.inl
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
hn : IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n
x : Fin (succ n) ↪ α
gx : M
x1 : Fin n ↪ ↥(SubMulActio... |
https://github.com/AntoineChambert-Loir/Jordan4.git | d49910c127be01229697737a55a2d756e908d3e1 | Jordan/MultipleTransitivity.lean | MulAction.stabilizer.isMultiplyPretransitive | [564, 1] | [631, 57] | specialize hgy ⟨i, hi'⟩ | case h.h.mk.inl
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
hn : IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n
x : Fin (succ n) ↪ α
gx : M
x1 : Fin n ↪ ↥(SubMulAction.ofStabilizer M a)
hga : gx • x (Fin.last n) = a
y : Fin (su... | case h.h.mk.inl
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
hn : IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n
x : Fin (succ n) ↪ α
gx : M
x1 : Fin n ↪ ↥(SubMulAction.ofStabilizer M a)
hga : gx • x (Fin.last n) = a
y : Fin (su... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.h.mk.inl
M : Type u_2
α : Type u_1
inst✝¹ : Group M
inst✝ : MulAction M α
hα' : IsPretransitive M α
n : ℕ
a : α
hn : IsMultiplyPretransitive (↥(stabilizer M a)) (↥(SubMulAction.ofStabilizer M a)) n
x : Fin (succ n) ↪ α
gx : M
x1 : Fin n ↪ ↥(SubMulActio... |
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