Theorem: conEvalHT (Pdl/Discon.lean)

State before:
X : List Formula
f : Formula
W : Type
M : KripkeModel W
w : W
⊢ evaluate M w (Con (f :: X)) ↔ evaluate M w f ∧ evaluate M w (Con X)
Tactic:
induction' X with g X _
State after:
case nil
f : Formula
W : Type
M : KripkeModel W
w : W
⊢ evaluate M w (Con [f]) ↔ evaluate M w f ∧ evaluate M w (Con [])

case cons
f : Formula
W : Type
M : KripkeModel W
w : W
g : Formula
X : List Formula
tail_ih✝ : evaluate M w (Con (f :: X)) ↔ evaluate M w f ∧ evaluate M w (Con X)
⊢ evaluate M w (Con (f :: g :: X)) ↔ evaluate M w f ∧ evaluate M w (Con (g :: X))

State before:
case nil
f : Formula
W : Type
M : KripkeModel W
w : W
⊢ evaluate M w (Con [f]) ↔ evaluate M w f ∧ evaluate M w (Con [])
Tactic:
simp
State after:
no goals

State before:
case cons
f : Formula
W : Type
M : KripkeModel W
w : W
g : Formula
X : List Formula
tail_ih✝ : evaluate M w (Con (f :: X)) ↔ evaluate M w f ∧ evaluate M w (Con X)
⊢ evaluate M w (Con (f :: g :: X)) ↔ evaluate M w f ∧ evaluate M w (Con (g :: X))
Tactic:
simp
State after:
no goals