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Proof step 44 from proof put-switch-primval-index-field (previous step)

st[r -- sks1] = refval(r1), st[r0 -- sks] = refval(r2), is_indexkey(sk), fits(r, sks1 + sk ', st), fits(r0, sks + mkfs(class, ty, fieldvar) ' ', st) ⊦ (st[r1 -- sk, val][(st[r1 -- sk, val][r0 -- sks]) .refval -- mkfs(class, ty, fieldvar) ', val0]) = (st[r2 -- mkfs(class, ty, fieldvar) ', val0][(st[r2 -- mkfs(class, ty, fieldvar) ', val0][r -- sks1]) .refval -- sk, val]), sk = mkfs(class, ty, fieldvar) ', junkref(str, r0, st), junkref(str, r, st), is_reftype(ty), is_referencevalue(st[r -- (sks1 + sk ')]), is_referencevalue(val0), is_referencevalue(val)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ is_indexkey(sk) ↔ (∃ i. sk = i ')
Proof step 43:
st[r -- sks1] = refval(r1), st[r0 -- sks] = refval(r2), ∃ i. sk = i ', fits(r, sks1 + sk ', st), fits(r0, sks + mkfs(class, ty, fieldvar) ' ', st) ⊦ (st[r1 -- sk, val][(st[r1 -- sk, val][r0 -- sks]) .refval -- mkfs(class, ty, fieldvar) ', val0]) = (st[r2 -- mkfs(class, ty, fieldvar) ', val0][(st[r2 -- mkfs(class, ty, fieldvar) ', val0][r -- sks1]) .refval -- sk, val]), sk = mkfs(class, ty, fieldvar) ', junkref(str, r0, st), junkref(str, r, st), is_reftype(ty), is_referencevalue(st[r -- (sks1 + sk ')]), is_referencevalue(val0), is_referencevalue(val)

Rule argument

[x0lemmaarg: spec-name: storekey instance-name: lemma-name: ex-04 antecedent: succedent: is_indexkey(sk) ↔ (∃ i. sk = i ') substlist: [sk] → [sk] add preconditions?: F is rewrite lemma?: T current spec?: F rotate lemma?: F replace all?: T paths: ((0, 0, 2)) dummy: () ]

Additional information

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