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Proof step 69 from proof validval-put-any (previous step)

validval(str, rk, val, st), validval(str, r -- mkfs(class, ty, fieldvar) ', val0, st) ⊦ r -- _type = rk, validval(str, val0, ty, st[rk, val]) ∧ ty ≠ void_type ∧ mkfs(class, ty, fieldvar) ' ≠ _length

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ 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 68:
validval(str, rk, val, st), ( is_fskey(mkfs(class, ty, fieldvar) ') → validval(str, val0, mkfs(class, ty, fieldvar) ' .fs .type, st) ∧ mkfs(class, ty, fieldvar) ' .fs .type ≠ void_type ∧ mkfs(class, ty, fieldvar) ' ≠ _length) ∧ (is_indexkey(mkfs(class, ty, fieldvar) ') → validval(str, val0, st[r -- _type] .type .type, st)) ⊦ r -- _type = rk, validval(str, val0, ty, st[rk, val]) ∧ ty ≠ void_type ∧ mkfs(class, ty, fieldvar) ' ≠ _length

Rule argument

[crewrite-arg: validrefkeyval-def , F , [st, val, sk, r, str] → [st, val0, mkfs(class, ty, fieldvar) ', r, str] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, val0, mkfs(class, ty, fieldvar) ', r, str)]]