apply Iff.intro
S : Stmt
s t : State
⊢ (S; Stmt.skip, s) ⟹ t ↔ (S, s) ⟹ t
case mp
S : Stmt
s t : State
⊢ (S; Stmt.skip, s) ⟹ t → (S, s) ⟹ t

case mpr
S : Stmt
s t : State
⊢ (S, s) ⟹ t → (S; Stmt.skip, s) ⟹ t