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Proof step 8 from proof add-in-09 (previous step)

sk ∈ fv ' + fis0, ∀ sk, r, class, st. sk ∈ fis0 → (addobj(r, class, fis0, st)[r -- sk]) = fis0[sk] ⊦ (addobj(r, class, fis0, st)[r -- fv .1, fv .2][r -- sk]) = (fv ' + fis0)[sk]

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
sk ∈ fv ' + fis0, ∀ sk, r, class, st. sk ∈ fis0 → (addobj(r, class, fis0, st)[r -- sk]) = fis0[sk] ⊦ ((sk = fv .1 ⊃ fv .2; addobj(r, class, fis0, st)[r -- sk])) = (fv ' + fis0)[sk]

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ r -- sk = r0 -- sk0 ↔ ¬ ¬ (r = r0 ∧ sk = sk0)], [CSIMPSEQ : ⊦ (st[rk0, val][rk]) = ((rk = rk0 ⊃ val; st[rk]))])]]