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Proof step 40 from proof validval-putrkvs (previous step)

sk .fs = mkfs(class, ty, fieldvar), validvals(str, rkvs, st), validval(str, r -- sk, val, st) ⊦ (is_fskey(sk) → validval(str, val, ty, st[rkvs]) ∧ ty ≠ void_type ∧ sk ≠ _length) ∧ (is_indexkey(sk) → validval(str, val, (st[rkvs][r -- _type]) .type .type, st[rkvs]))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ validval(str, r -- sk, val, st) ↔ (is_fskey(sk) → validval(str, val, sk .fs .type, st) ∧ sk .fs .type ≠ void_type ∧ sk ≠ _length) ∧ (is_indexkey(sk) → validval(str, val, st[r -- _type] .type .type, st))
Proof step 39:
sk .fs = mkfs(class, ty, fieldvar), validvals(str, rkvs, st), (is_fskey(sk) → validval(str, val, sk .fs .type, st) ∧ sk .fs .type ≠ void_type ∧ sk ≠ _length) ∧ (is_indexkey(sk) → validval(str, val, st[r -- _type] .type .type, st)) ⊦ (is_fskey(sk) → validval(str, val, ty, st[rkvs]) ∧ ty ≠ void_type ∧ sk ≠ _length) ∧ (is_indexkey(sk) → validval(str, val, (st[rkvs][r -- _type]) .type .type, st[rkvs]))

Rule argument

[crewrite-arg: validrefkeyval-def , F , [st, val, sk, r, str] → [st, val, sk, r, str] ]

Additional information

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