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Proof step 26 from proof ac-lookup-05 (previous step)

is_indexkey(sk), ∀ sk0, class0, st0, r0. ¬ is_fskey(sk0) → (addclass(class0, fis0, st0)[r0 -- sk0]) = st0[r0 -- sk0] ⊦ (addclass(class, (sk0 × val) ' + fis0, st)[r -- sk]) = st[r -- sk]

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ is_indexkey(fv .1) → addclass(class, fv ' + fis, st) = addclass(class, fis, st)
Proof step 23:
¬ is_indexkey((sk0 × val) .1), is_indexkey(sk), ∀ sk0, class0, st0, r0. ¬ is_fskey(sk0) → (addclass(class0, fis0, st0)[r0 -- sk0]) = st0[r0 -- sk0] ⊦ (addclass(class, (sk0 × val) ' + fis0, st)[r -- sk]) = st[r -- sk]
Proof step 25:
is_indexkey((sk0 × val) .1), is_indexkey(sk), ∀ sk0, class0, st0, r0. ¬ is_fskey(sk0) → (addclass(class0, fis0, st0)[r0 -- sk0]) = st0[r0 -- sk0] ⊦ (addclass(class, fis0, st)[r -- sk]) = st[r -- sk]

Rule argument

[crewrite-arg: ac-no2 , F , [st, fis, fv, class] → [st, fis0, sk0 × val, class] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, fis0, sk0 × val, class)]]