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Proof step 26 from proof ac-in-11 (previous step)

∀ sk, r, class, st. ¬ is_fskey(sk) → (r -- sk ∈ addclass(class, fis0, st) ↔ r -- sk ∈ st) ⊦ ¬ is_fskey(sk) → (r -- sk ∈ addclass(class, fv + fis0, st) ↔ r -- sk ∈ st)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
⊦ rk ∈ st → rk ∈ addclass(class, fis, st)
Proof step 25:
r -- sk ∈ addclass(class, fv ' + fis0, st), is_indexkey(sk), r ∈ addclass(class, fv ' + fis0, st), ∀ sk0, r0, class0, st0. ¬ is_fskey(sk0) → (r0 -- sk0 ∈ addclass(class0, fis0, st0) → r0 -- sk0 ∈ st0) ⊦ r -- sk ∈ st

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPFORWARD : ⊦ r -- sk ∈ st → r ∈ st], [CSIMPSEQ : ⊦ ¬ is_fskey(sk) ↔ is_indexkey(sk)], [CSIMPSEQ : ⊦ fv + fis = fv ' + fis])]]