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Proof step 54 from proof put-switch-primval-index-field (previous step)

sks0 .last = mkfs(class, ty, fieldvar) ', is_indexkey(sk), fits(r, sks1 + sk ', st), fits(r0, sks0, st) ⊦ (st[r -- (sks1 + sk '), val][r0 -- sks0, val0]) = (st[r0 -- sks0, val0][r -- (sks1 + sk '), val]), sks0 = [], 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 elim lemma

And obtained the following new goals

Proof step 53:
sks0 = sks + sk0 ', sk0 = mkfs(class, ty, fieldvar) ', is_indexkey(sk), fits(r, sks1 + sk ', st), fits(r0, sks0, st) ⊦ (st[r -- (sks1 + sk '), val][r0 -- sks0, val0]) = (st[r0 -- sks0, val0][r -- (sks1 + sk '), val]), sks0 = [], 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: list-last instance-name: storekeys lemma-name: last-elim antecedent: sks ≠ [] succedent: sk = sks .last ∧ sks0 = sks .butlast ↔ sks = sks0 + sk ' substlist: [sks, sk, sks0] → [sks0, sk0, sks] add preconditions?: F is rewrite lemma?: F current spec?: F rotate lemma?: F replace all?: F paths: () dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : sks ≠ [] ⊦ sk = sks .last ∧ sks0 = sks .butlast ↔ sks = sks0 + sk '])], [EXTRATERMS : (sks0, sk0, sks)]]