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Proof step 21 from proof validval-put-any (previous step)

validref(str, r0, ty, st), is_reftype(ty), validval(str, r1 -- mkfs(class0, ty0, fieldvar0) ', val, st), r ≠ r1 ∨ _type ≠ mkfs(class0, ty0, fieldvar0) ' ⊦ ty = void_type, mkfs(class, ty, fieldvar) ' = _length, validref(str, r0, ty, st[r1 -- mkfs(class0, ty0, fieldvar0) ', val]), (is_referencevalue(val) → validref(str, val .refval, ty0, st) ∧ is_reftype(ty0)) ∧ (¬ is_referencevalue(val) → okval(val, ty0) ∧ ty0 ≠ void_type ∧ mkfs(class0, ty0, fieldvar0) ' ≠ _length)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 14:
⊦ 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 20:
validref(str, r0, ty, st), is_reftype(ty), ( is_fskey(mkfs(class0, ty0, fieldvar0) ') → validval(str, val, mkfs(class0, ty0, fieldvar0) ' .fs .type, st) ∧ mkfs(class0, ty0, fieldvar0) ' .fs .type ≠ void_type ∧ mkfs(class0, ty0, fieldvar0) ' ≠ _length) ∧ (is_indexkey(mkfs(class0, ty0, fieldvar0) ') → validval(str, val, st[r1 -- _type] .type .type, st)), r ≠ r1 ∨ _type ≠ mkfs(class0, ty0, fieldvar0) ' ⊦ ty = void_type, mkfs(class, ty, fieldvar) ' = _length, validref(str, r0, ty, st[r1 -- mkfs(class0, ty0, fieldvar0) ', val]), (is_referencevalue(val) → validref(str, val .refval, ty0, st) ∧ is_reftype(ty0)) ∧ (¬ is_referencevalue(val) → okval(val, ty0) ∧ ty0 ≠ void_type ∧ mkfs(class0, ty0, fieldvar0) ' ≠ _length)

Rule argument

[crewrite-arg: validrefkeyval-def , F , [st, val, sk, r, str] → [st, val, mkfs(class0, ty0, fieldvar0) ', r1, str] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, val, mkfs(class0, ty0, fieldvar0) ', r1, str)]]