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Proof step 33 from proof validval-put-any (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 29:
⊦ is_indexkey(sk) ↔ (∃ i. sk = i ')
Proof step 32:
sk .fs = mkfs(class0, ty0, fieldvar0), validref(str, r0, ty, st), is_reftype(ty), ∃ i. sk = i ', okval(refval(r2), st[r1 -- _type] .type .type), validref(str, r2, st[r1 -- _type] .type .type, st), r ≠ r1 ∨ _type ≠ sk ⊦ is_arraytype(st[r1 -- _type] .type), ty = void_type, mkfs(class, ty, fieldvar) ' = _length, validref(str, r0, ty, st[r1 -- sk, refval(r2)])

Rule argument

[speclemmaarg: ,is_indexkey(sk) ↔ (∃ i. sk = i ') ,[sk] → [sk] ,F ,storekey , ,ex-04 ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (sk)]]