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Proof step 9 from proof add-nput-01 (previous step)

∀ r, class1, sk, val, fis0, st. addobj(r, class1, fis1 + (sk × val) ' + fis0, st) = (addobj(r, class1, fis1 + fis0, st)[r -- sk, val]) ∨ sk ∈ fis1 ⊦ addobj(r, class1, (fv + fis1) + (sk × val) ' + fis0, st) = (addobj(r, class1, (fv + fis1) + fis0, st)[r -- sk, val]), sk ∈ fv + fis1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
⊦ addobj(r, class1, fv ' + fis, st) = (addobj(r, class1, fis, st)[r -- fv .1, fv .2])
Proof step 8:
∀ r, class1, sk, val, fis0, st. addobj(r, class1, fis1 + (sk × val) ' + fis0, st) = (addobj(r, class1, fis1 + fis0, st)[r -- sk, val]) ∨ sk ∈ fis1 ⊦ (addobj(r, class1, fis1 + (sk × val) ' + fis0, st)[r -- fv .1, fv .2]) = (addobj(r, class1, fis1 + fis0, st)[r -- fv .1, fv .2][r -- sk, val]), sk ∈ fv ', sk ∈ fis1

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ sk ∈ fis + fis0 ↔ sk ∈ fis ∨ sk ∈ fis0], [CSIMPSEQ : ⊦ (fis + fis0) + fis1 = fis + fis0 + fis1], [CSIMPSEQ : ⊦ fv + fis = fv ' + fis])]]