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Proof step 22 from proof validfieldinits-rec (previous step)

sk .fs = mkfs(class, ty, fieldvar) ⊦ validfieldinits(str, (sk × val) ' + fis, st) ↔ ¬ is_indexkey(sk) ∧ validval(str, val, ty, st) ∧ type∃(str, ty) ∧ validfieldinits(str, fis, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 1:
⊦ validfieldinits(str, fis, st) ↔ (∀ sk, val. sk × val ∈ fis → is_fskey(sk) ∧ type∃(str, sk .fs .type) ∧ validval(str, val, sk .fs .type, st))
Proof step 21:
sk .fs = mkfs(class, ty, fieldvar) ⊦ validfieldinits(str, (sk × val) ' + fis, st) ↔ ¬ is_indexkey(sk) ∧ validval(str, val, ty, st) ∧ type∃(str, ty) ∧ (∀ sk, val. sk × val ∈ fis → is_fskey(sk) ∧ type∃(str, sk .fs .type) ∧ validval(str, val, sk .fs .type, st))

Rule argument

[crewrite-arg: validfieldinits-def , F , [st, fis, str] → [st, fis, str] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, fis, str)]]