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Proof step 101 from proof validval-put-any (previous step)

sk .fs = mkfs(class, ty, fieldvar), sk0 .fs = mkfs(class0, ty0, fieldvar0), validref(str, r0, st[r -- _type] .type .type, st), okval(refval(r0), st[r -- _type] .type .type), is_indexkey(sk), is_indexkey(sk0), okval(refval(r2), st[r1 -- _type] .type .type), validref(str, r2, st[r1 -- _type] .type .type, st), r ≠ r1 ∨ _type ≠ sk0 ⊦ is_arraytype(st[r1 -- _type] .type), validref(str, r0, st[r -- _type] .type .type, st[r1 -- sk0, refval(r2)])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 97:
⊦ is_indexkey(sk) ↔ (∃ i. sk = i ')
Proof step 100:
sk .fs = mkfs(class, ty, fieldvar), sk0 .fs = mkfs(class0, ty0, fieldvar0), validref(str, r0, st[r -- _type] .type .type, st), okval(refval(r0), st[r -- _type] .type .type), is_indexkey(sk), ∃ i. sk0 = i ', okval(refval(r2), st[r1 -- _type] .type .type), validref(str, r2, st[r1 -- _type] .type .type, st), r ≠ r1 ∨ _type ≠ sk0 ⊦ is_arraytype(st[r1 -- _type] .type), validref(str, r0, st[r -- _type] .type .type, st[r1 -- sk0, refval(r2)])

Rule argument

[speclemmaarg: ,is_indexkey(sk) ↔ (∃ i. sk = i ') ,[sk] → [sk0] ,F ,storekey , ,ex-04 ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (sk0)]]