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Proof step 27 from proof ac-mode-01 (previous step)

∀ class0, st0. (addclass(class0, fis0, st0)[_mode]) = st0[_mode] ⊦ (addclass(class, fv ' + fis0, st)[_mode]) = st[_mode], mkfs(`java.lang.Object' .class, void_type, `mode' .field) ' ∈ fv ', mkfs(`java.lang.Object' .class, void_type, `mode' .field) ' ∈ fis0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ is_fskey(fv .1) ∧ fv .1 .fs .class ≠ class → addclass(class, fv ' + fis, st) = addclass(class, fis, st)
Proof step 17:
¬ (is_fskey(fv .1) ∧ fv .1 .fs .class ≠ class), ∀ class0, st0. (addclass(class0, fis0, st0)[_mode]) = st0[_mode] ⊦ (addclass(class, fv ' + fis0, st)[_mode]) = st[_mode], mkfs(`java.lang.Object' .class, void_type, `mode' .field) ' ∈ fv ', mkfs(`java.lang.Object' .class, void_type, `mode' .field) ' ∈ fis0
Proof step 26:
is_fskey(fv .1) ∧ fv .1 .fs .class ≠ class, ∀ class0, st0. (addclass(class0, fis0, st0)[_mode]) = st0[_mode] ⊦ (addclass(class, fis0, st)[_mode]) = st[_mode], mkfs(`java.lang.Object' .class, void_type, `mode' .field) ' ∈ fv ', mkfs(`java.lang.Object' .class, void_type, `mode' .field) ' ∈ fis0

Rule argument

[crewrite-arg: ac-no1 , F , [st, fis, fv, class] → [st, fis0, fv, class] ]

Additional information

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