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Proof step 55 from proof validfieldinits-def-01 (previous step)

∀ str, st. validfieldinits(str, fis0, st) ↔ validfieldinits(fis0, st) ∧ ¬ junkrefs(str, fis0 .vals, st) ∧ (∀ sk. sk ∈ fis0 → type∃(str, sk .fs .type)) ⊦ validfieldinits(str, (sk0 × val) ' + fis0, st) ↔ validfieldinits((sk0 × val) ' + fis0, st) ∧ ¬ junkrefs(str, val ' + fis0 .vals, st) ∧ (∀ sk. sk ∈ (sk0 × val) ' + fis0 → type∃(str, sk .fs .type))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ validfieldinits(str, fv ' + fis, st) ↔ is_fskey(fv .1) ∧ validval(str, fv .2, fv .1 .fs .type, st) ∧ type∃(str, fv .1 .fs .type) ∧ validfieldinits(str, fis, st)
Proof step 54:
∀ str, st. validfieldinits(str, fis0, st) ↔ validfieldinits(fis0, st) ∧ ¬ junkrefs(str, fis0 .vals, st) ∧ (∀ sk. sk ∈ fis0 → type∃(str, sk .fs .type)) ⊦ is_fskey((sk0 × val) .1) ∧ validval(str, (sk0 × val) .2, (sk0 × val) .1 .fs .type, st) ∧ type∃(str, (sk0 × val) .1 .fs .type) ∧ validfieldinits(str, fis0, st) ↔ validfieldinits((sk0 × val) ' + fis0, st) ∧ ¬ junkrefs(str, val ' + fis0 .vals, st) ∧ (∀ sk. sk ∈ (sk0 × val) ' + fis0 → type∃(str, sk .fs .type))

Rule argument

[crewrite-arg: validfieldinits-rec , F , [st, fis, fv, str] → [st, fis0, sk0 × val, str] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, fis0, sk0 × val, str)]]