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Proof step 29 from proof ac-lookup (previous step)

mkfs(class1, ty, fieldvar) ' ∈ fv ' + fis0, ∀ class1, ty, fieldvar, st. mkfs(class1, ty, fieldvar) ' ∈ fis0 → (addclass(class1, fis0, st)[jvmref -- mkfs(class1, ty, fieldvar) ']) = fis0[mkfs(class1, ty, fieldvar) '] ⊦ (addclass(class1, fv ' + fis0, st)[jvmref -- mkfs(class1, ty, fieldvar) ']) = (fv ' + fis0)[mkfs(class1, ty, fieldvar) ']

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ is_indexkey(fv .1) → addclass(class, fv ' + fis, st) = addclass(class, fis, st)
Proof step 22:
¬ is_indexkey(fv .1), mkfs(class1, ty, fieldvar) ' ∈ fv ' + fis0, ∀ class1, ty, fieldvar, st. mkfs(class1, ty, fieldvar) ' ∈ fis0 → (addclass(class1, fis0, st)[jvmref -- mkfs(class1, ty, fieldvar) ']) = fis0[mkfs(class1, ty, fieldvar) '] ⊦ (addclass(class1, fv ' + fis0, st)[jvmref -- mkfs(class1, ty, fieldvar) ']) = (fv ' + fis0)[mkfs(class1, ty, fieldvar) ']
Proof step 28:
is_indexkey(fv .1), mkfs(class1, ty, fieldvar) ' ∈ fv ' + fis0, ∀ class1, ty, fieldvar, st. mkfs(class1, ty, fieldvar) ' ∈ fis0 → (addclass(class1, fis0, st)[jvmref -- mkfs(class1, ty, fieldvar) ']) = fis0[mkfs(class1, ty, fieldvar) '] ⊦ (addclass(class1, fis0, st)[jvmref -- mkfs(class1, ty, fieldvar) ']) = (fv ' + fis0)[mkfs(class1, ty, fieldvar) ']

Rule argument

[crewrite-arg: ac-no2 , F , [st, fis, fv, class] → [st, fis0, fv, class1] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, fis0, fv, class1)]]