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Proof step 137 from proof compat-addclass (previous step)

sk .fs = mkfs(class1, ty, fieldvar), st[r -- _type] = typeval(mkclasstype(class0)), fis .keys = statfields(class), sk ∈ instfields(class0), compatmode(str, st), compatstatic(str, st), okfieldinits(class, fis), r -- _type ∈ st, r ∈ st, compatfields(str, r, instfields(class0), st), class+∃(str, class0) ⊦ r = jvmref, r -- sk ∈ addclass(class, fis, st) ∧ ¬ is_indexkey(sk) ∧ compat(str, st[r -- sk], ty, addclass(class, fis, st))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 134:
⊦ compatfields(str, r, sks, st) ↔ (∀ sk. sk ∈ sks → r -- sk ∈ st ∧ is_fskey(sk) ∧ compat(str, st[r -- sk], sk .fs .type, st))
Proof step 136:
sk .fs = mkfs(class1, ty, fieldvar), st[r -- _type] = typeval(mkclasstype(class0)), fis .keys = statfields(class), sk ∈ instfields(class0), compatmode(str, st), compatstatic(str, st), okfieldinits(class, fis), r -- _type ∈ st, r ∈ st, ∀ sk. sk ∈ instfields(class0) → r -- sk ∈ st ∧ is_fskey(sk) ∧ compat(str, st[r -- sk], sk .fs .type, st), class+∃(str, class0) ⊦ r = jvmref, r -- sk ∈ addclass(class, fis, st) ∧ ¬ is_indexkey(sk) ∧ compat(str, st[r -- sk], ty, addclass(class, fis, st))

Rule argument

[crewrite-arg: fields-compat , F , [st, sks, r, str] → [st, instfields(class0), r, str] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, instfields(class0), r, str)]]