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Proof step 22 from proof okarrays-all (conclusion)

⊦ okarrays(r, fis, st) ↔ (∀ sk, val. sk × val ∈ fis → is_integervalue(val) ∧ is_fskey(sk) ∧ is_arraytype(sk .fs .type) ∧ okarray(st[r -- sk], sk .fs .type .type, val .intval, st))

User applied rule structural induction

And obtained the following new goals

Proof step 1:
⊦ okarrays(r, [], st)
Proof step 21:
∀ r, st. okarrays(r, fis0, st) ↔ (∀ sk, val. sk × val ∈ fis0 → is_integervalue(val) ∧ is_fskey(sk) ∧ is_arraytype(sk .fs .type) ∧ okarray(st[r -- sk], sk .fs .type .type, val .intval, st)) ⊦ okarrays(r, fv + fis0, st) ↔ (∀ sk, val. sk × val ∈ fv + fis0 → is_integervalue(val) ∧ is_fskey(sk) ∧ is_arraytype(sk .fs .type) ∧ okarray(st[r -- sk], sk .fs .type .type, val .intval, st))

Rule argument

[VARWITHVARSEQSARG : fis, ()]

Additional information

[[CONCRETESIMPRULES : ([CSIMPGEN : fieldinits generated by [], +;], [CSIMPSEQ : ⊦ ¬ fv ∈ []])]]