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Proof step 5 from proof okarrays-one-01 (previous step)

sk .fs = mkfs(class, ty, fieldvar) ⊦ okarrays(r, (sk × val) ', st) ↔ is_integervalue(val) ∧ ¬ is_indexkey(sk) ∧ is_arraytype(ty) ∧ okarray(st[r -- sk], ty .type, val .intval, st)

User applied rule insert lemma

And obtained the following new goals

Proof step 1:
⊦ okarrays(r, (sk × val) ' + fis, st) ↔ is_integervalue(val) ∧ is_fskey(sk) ∧ is_arraytype(sk .fs .type) ∧ okarray(st[r -- sk], sk .fs .type .type, val .intval, st) ∧ okarrays(r, fis, st)
Proof step 4:
okarrays(r, (sk × val) ' + [], st) ↔ is_integervalue(val) ∧ is_fskey(sk) ∧ is_arraytype(sk .fs .type) ∧ okarray(st[r -- sk], sk .fs .type .type, val .intval, st) ∧ okarrays(r, [], st), sk .fs = mkfs(class, ty, fieldvar) ⊦ okarrays(r, (sk × val) ', st) ↔ is_integervalue(val) ∧ ¬ is_indexkey(sk) ∧ is_arraytype(ty) ∧ okarray(st[r -- sk], ty .type, val .intval, st)

Rule argument

[LEMMAARG : okarrays-rec, [r, sk, val, fis, st] → [r, sk, val, [], st]]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (r, sk, val, [], st)]]