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Proof step 52 from proof put-switch-primval-index-field (previous step)

is_indexkey(sk), fits(r, sks1 + sk ', st), fits(r0, sks + mkfs(class, ty, fieldvar) ' ', st) ⊦ (st[r -- (sks1 + sk '), val][r0 -- (sks + mkfs(class, ty, fieldvar) ' '), val0]) = (st[r0 -- (sks + mkfs(class, ty, fieldvar) ' '), val0][r -- (sks1 + 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 1:
⊦ st[r -- (sks + sk '), val] = st[st[r -- sks] .refval -- sk, val]
Proof step 51:
is_indexkey(sk), fits(r, sks1 + sk ', st), fits(r0, sks + mkfs(class, ty, fieldvar) ' ', st) ⊦ (st[st[r -- sks1] .refval -- sk, val][r0 -- (sks + mkfs(class, ty, fieldvar) ' '), val0]) = (st[r0 -- (sks + mkfs(class, ty, fieldvar) ' '), val0][r -- (sks1 + 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: storefuns instance-name: lemma-name: put-last-rec-better antecedent: succedent: st[r -- (sks + sk '), val] = st[st[r -- sks] .refval -- sk, val] substlist: [val, sk, sks, r, st] → [val, sk, sks1, r, st] add preconditions?: F is rewrite lemma?: T current spec?: F rotate lemma?: F replace all?: T paths: ((1, 0, 0, 1, 0, 1, 0)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (val, sk, sks1, r, st)]]