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Proof step 5 from proof addclass-update-sw (previous step)

update(r, fis1, addclass(class0, fis0, st)) = addclass(class0, fis0, update(r, fis1, st)), ∀ r, class0, fis0, st. r = jvmref ∨ update(r, fis1, addclass(class0, fis0, st)) = addclass(class0, fis0, update(r, fis1, st)) ⊦ r = jvmref, (addclass(class0, fis0, update(r, fis1, st))[r -- sk, val]) = addclass(class0, fis0, update(r, (sk × val) ' + fis1, st))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ update(r, (sk × val) ' + fis, st) = (update(r, fis, st)[r -- sk, val])
Proof step 4:
update(r, fis1, addclass(class0, fis0, st)) = addclass(class0, fis0, update(r, fis1, st)), ∀ r, class0, fis0, st. r = jvmref ∨ update(r, fis1, addclass(class0, fis0, st)) = addclass(class0, fis0, update(r, fis1, st)) ⊦ r = jvmref, (addclass(class0, fis0, update(r, fis1, st))[r -- sk, val]) = addclass(class0, fis0, update(r, fis1, st)[r -- sk, val])

Rule argument

[speclemmaarg: , update(r, (sk × val) ' + fis, st) = (update(r, fis, st)[r -- sk, val]) ,[st, fis, val, sk, r] → [st, fis1, val, sk, r] ,F ,okfuns , ,update-rec ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, fis1, val, sk, r)]]