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Proof step 37 from proof ac-shift-03 (previous step)

∀ class, st, ty, fieldvar, val. (addclass(class, fis0, st)[jvmref -- mkfs(class, ty, fieldvar) ', val]) = addclass(class, fis0[mkfs(class, ty, fieldvar) ', val], st) ⊦ (addclass(class, fv ' + fis0, st)[jvmref -- mkfs(class, ty, fieldvar) ', val]) = addclass(class, (fv ' + fis0)[mkfs(class, ty, fieldvar) ', val], st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ is_indexkey(fv .1) → addclass(class, fv ' + fis, st) = addclass(class, fis, st)
Proof step 30:
¬ is_indexkey(fv .1), ∀ class, st, ty, fieldvar, val. (addclass(class, fis0, st)[jvmref -- mkfs(class, ty, fieldvar) ', val]) = addclass(class, fis0[mkfs(class, ty, fieldvar) ', val], st) ⊦ (addclass(class, fv ' + fis0, st)[jvmref -- mkfs(class, ty, fieldvar) ', val]) = addclass(class, (fv ' + fis0)[mkfs(class, ty, fieldvar) ', val], st)
Proof step 36:
is_indexkey(fv .1), ∀ class, st, ty, fieldvar, val. (addclass(class, fis0, st)[jvmref -- mkfs(class, ty, fieldvar) ', val]) = addclass(class, fis0[mkfs(class, ty, fieldvar) ', val], st) ⊦ (addclass(class, fis0, st)[jvmref -- mkfs(class, ty, fieldvar) ', val]) = addclass(class, (fv ' + fis0)[mkfs(class, ty, fieldvar) ', val], st)

Rule argument

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

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, fis0, fv, class)]]