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Proof step 20 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) ∧ (∀ sk0, val0. sk0 × val0 ∈ fis → ¬ is_indexkey(sk0) ∧ type∃(str, sk0 .fs .type) ∧ validval(str, val0, sk0 .fs .type, st))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ 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 19:
sk .fs = mkfs(class, ty, fieldvar) ⊦ (∀ sk0, val0. sk0 × val0 ∈ (sk × val) ' + fis → is_fskey(sk0) ∧ type∃(str, sk0 .fs .type) ∧ validval(str, val0, sk0 .fs .type, st)) ↔ ¬ is_indexkey(sk) ∧ validval(str, val, ty, st) ∧ type∃(str, ty) ∧ (∀ sk0, val0. sk0 × val0 ∈ fis → ¬ is_indexkey(sk0) ∧ type∃(str, sk0 .fs .type) ∧ validval(str, val0, sk0 .fs .type, st))

Rule argument

[crewrite-arg: validfieldinits-def , F , [st, fis, str] → [st, (sk × val) ' + fis, str] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, (sk × val) ' + fis, str)]]