Theorem: BunchImpl.PreEquiv.prop_left (BunchImpl/Equiv.lean)

State before:
P✝ : Sort u_1
A : Typ P✝
B : Bunch P✝
⊢ ¬PreEquiv (prop A) B
Tactic:
intro h
State after:
P✝ : Sort u_1
A : Typ P✝
B : Bunch P✝
h : PreEquiv (prop A) B
⊢ False

State before:
P✝ : Sort u_1
A : Typ P✝
B : Bunch P✝
h : PreEquiv (prop A) B
⊢ False
Tactic:
generalize hA' : prop A = A' at h
State after:
P✝ : Sort u_1
A : Typ P✝
B A' : Bunch P✝
hA' : prop A = A'
h : PreEquiv A' B
⊢ False

State before:
P✝ : Sort u_1
A : Typ P✝
B A' : Bunch P✝
hA' : prop A = A'
h : PreEquiv A' B
⊢ False
Tactic:
induction h <;> simp at hA'
State after:
case subbunch
P✝ : Sort u_1
A : Typ P✝
B A' : Bunch P✝
h✝ : BunchWithHole P✝
b1✝ b2✝ : Bunch P✝
a✝ : PreEquiv b1✝ b2✝
a_ih✝ : prop A = b1✝ → False
hA' : h✝ = BunchWithHole.hole ∧ b1✝ = prop A
⊢ False

State before:
case subbunch
P✝ : Sort u_1
A : Typ P✝
B A' : Bunch P✝
h✝ : BunchWithHole P✝
b1✝ b2✝ : Bunch P✝
a✝ : PreEquiv b1✝ b2✝
a_ih✝ : prop A = b1✝ → False
hA' : h✝ = BunchWithHole.hole ∧ b1✝ = prop A
⊢ False
Tactic:
rcases hA' with ⟨rfl,rfl⟩
State after:
case subbunch.intro
P✝ : Sort u_1
A : Typ P✝
B A' b2✝ : Bunch P✝
a✝ : PreEquiv (prop A) b2✝
a_ih✝ : prop A = prop A → False
⊢ False

State before:
case subbunch.intro
P✝ : Sort u_1
A : Typ P✝
B A' b2✝ : Bunch P✝
a✝ : PreEquiv (prop A) b2✝
a_ih✝ : prop A = prop A → False
⊢ False
Tactic:
simp at *
State after:
no goals