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Proof step 84 from proof validval-put-any (previous step)

sk .fs = mkfs(class, ty, fieldvar), validval(str, r1 -- mkfs(class0, ty0, fieldvar0) ', refval(r2), st), is_indexkey(sk), okval(refval(r0), st[r -- _type] .type .type), validref(str, r0, st[r -- _type] .type .type, st), r ≠ r1 ∨ _type ≠ mkfs(class0, ty0, fieldvar0) ' ⊦ validref(str, r0, st[r -- _type] .type .type, st[r1 -- mkfs(class0, ty0, fieldvar0) ', refval(r2)]), validref(str, r2, ty0, st) ∧ is_reftype(ty0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 79:
⊦ 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 83:
sk .fs = mkfs(class, ty, fieldvar), ( is_fskey(mkfs(class0, ty0, fieldvar0) ') → validval(str, refval(r2), 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, refval(r2), st[r1 -- _type] .type .type, st)), is_indexkey(sk), okval(refval(r0), st[r -- _type] .type .type), validref(str, r0, st[r -- _type] .type .type, st), r ≠ r1 ∨ _type ≠ mkfs(class0, ty0, fieldvar0) ' ⊦ validref(str, r0, st[r -- _type] .type .type, st[r1 -- mkfs(class0, ty0, fieldvar0) ', refval(r2)]), validref(str, r2, ty0, st) ∧ is_reftype(ty0)

Rule argument

[crewrite-arg: validrefkeyval-def , F , [st, val, sk, r, str] → [st, refval(r2), mkfs(class0, ty0, fieldvar0) ', r1, str] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, refval(r2), mkfs(class0, ty0, fieldvar0) ', r1, str)]]