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Proof step 9 from proof add-notin (previous step)

∀ sk, r, class, st. sk = _type ∨ (addobj(r, class, fis0, st)[r -- sk]) = st[r -- sk] ∨ sk ∈ fis0 ⊦ sk = _type, ((sk = fv .1 ⊃ fv .2; addobj(r, class, fis0, st)[r -- sk])) = st[r -- sk], sk ∈ fv ', sk ∈ fis0

Heuristic if-then-else split applied rule case distinction

And obtained the following new goals

Proof step 4:
sk = fv .1, ∀ sk, r, class, st. sk = _type ∨ (addobj(r, class, fis0, st)[r -- sk]) = st[r -- sk] ∨ sk ∈ fis0 ⊦ fv .2 = st[r -- sk], sk = _type, sk ∈ fv ', sk ∈ fis0
Proof step 8:
sk ≠ fv .1, ∀ sk, r, class, st. sk = _type ∨ (addobj(r, class, fis0, st)[r -- sk]) = st[r -- sk] ∨ sk ∈ fis0 ⊦ (addobj(r, class, fis0, st)[r -- sk]) = st[r -- sk], sk = _type, sk ∈ fv ', sk ∈ fis0

Rule argument

[CASEDARG : pos: right 2, ()]

Additional information

[[CONCRETESIMPRULES : ()]]