Theorem: WType.mkL_inversion (Logic/Vorspiel/W.lean)

State before:
α : Type u_1
β : α → Type u_2
inst✝⁴ : Primcodable α
inst✝³ : (a : α) → Fintype (β a)
inst✝² : (a : α) → DecidableEq (β a)
inst✝¹ : (a : α) → Primcodable (β a)
inst✝ : PrimrecCard β
w : WType β
⊢ mkL w.inversion.1 w.inversion.2 = some w
Tactic:
rcases w with ⟨a, f⟩
State after:
case mk
α : Type u_1
β : α → Type u_2
inst✝⁴ : Primcodable α
inst✝³ : (a : α) → Fintype (β a)
inst✝² : (a : α) → DecidableEq (β a)
inst✝¹ : (a : α) → Primcodable (β a)
inst✝ : PrimrecCard β
a : α
f : β a → WType β
⊢ mkL (mk a f).inversion.1 (mk a f).inversion.2 = some (mk a f)

State before:
case mk
α : Type u_1
β : α → Type u_2
inst✝⁴ : Primcodable α
inst✝³ : (a : α) → Fintype (β a)
inst✝² : (a : α) → DecidableEq (β a)
inst✝¹ : (a : α) → Primcodable (β a)
inst✝ : PrimrecCard β
a : α
f : β a → WType β
⊢ mkL (mk a f).inversion.1 (mk a f).inversion.2 = some (mk a f)
Tactic:
simp[inversion, mkL]
State after:
case mk
α : Type u_1
β : α → Type u_2
inst✝⁴ : Primcodable α
inst✝³ : (a : α) → Fintype (β a)
inst✝² : (a : α) → DecidableEq (β a)
inst✝¹ : (a : α) → Primcodable (β a)
inst✝ : PrimrecCard β
a : α
f : β a → WType β
⊢ (fintypeArrowEquivFinArrow.symm fun i => f (fintypeEquivFin.symm i)) = f

State before:
case mk
α : Type u_1
β : α → Type u_2
inst✝⁴ : Primcodable α
inst✝³ : (a : α) → Fintype (β a)
inst✝² : (a : α) → DecidableEq (β a)
inst✝¹ : (a : α) → Primcodable (β a)
inst✝ : PrimrecCard β
a : α
f : β a → WType β
⊢ (fintypeArrowEquivFinArrow.symm fun i => f (fintypeEquivFin.symm i)) = f
Tactic:
funext
State after:
case mk.h
α : Type u_1
β : α → Type u_2
inst✝⁴ : Primcodable α
inst✝³ : (a : α) → Fintype (β a)
inst✝² : (a : α) → DecidableEq (β a)
inst✝¹ : (a : α) → Primcodable (β a)
inst✝ : PrimrecCard β
a : α
f : β a → WType β
x✝ : β a
⊢ fintypeArrowEquivFinArrow.symm (fun i => f (fintypeEquivFin.symm i)) x✝ = f x✝

State before:
case mk.h
α : Type u_1
β : α → Type u_2
inst✝⁴ : Primcodable α
inst✝³ : (a : α) → Fintype (β a)
inst✝² : (a : α) → DecidableEq (β a)
inst✝¹ : (a : α) → Primcodable (β a)
inst✝ : PrimrecCard β
a : α
f : β a → WType β
x✝ : β a
⊢ fintypeArrowEquivFinArrow.symm (fun i => f (fintypeEquivFin.symm i)) x✝ = f x✝
Tactic:
simp
State after:
no goals