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Proof step 51 from proof put-switch-primval-field-field (previous step)

sks0 .last = mkfs(class0, ty0, fieldvar0) ', fits(r0, sks0, st), fits(r, sks1 + mkfs(class, ty, fieldvar) ' ', st), st[r -- sks1] ≠ st[r0 -- sks0 .butlast] ∨ class ≠ class0 ∨ ty ≠ ty0 ∨ fieldvar ≠ fieldvar0 ⊦ sks0 = [], (st[r -- (sks1 + mkfs(class, ty, fieldvar) ' '), val][r0 -- sks0, val0]) = (st[r0 -- sks0, val0][r -- (sks1 + mkfs(class, ty, fieldvar) ' '), val]), is_referencevalue(val), is_referencevalue(val0), is_reftype(ty), is_reftype(ty0), junkref(str, r, st), junkref(str, r0, st)

User applied rule insert elim lemma

And obtained the following new goals

Proof step 50:
sks0 = sks + sk ', sk = mkfs(class0, ty0, fieldvar0) ', fits(r0, sks0, st), fits(r, sks1 + mkfs(class, ty, fieldvar) ' ', st), st[r -- sks1] ≠ st[r0 -- sks] ∨ class ≠ class0 ∨ ty ≠ ty0 ∨ fieldvar ≠ fieldvar0 ⊦ sks0 = [], (st[r -- (sks1 + mkfs(class, ty, fieldvar) ' '), val][r0 -- sks0, val0]) = (st[r0 -- sks0, val0][r -- (sks1 + mkfs(class, ty, fieldvar) ' '), val]), is_referencevalue(val), is_referencevalue(val0), is_reftype(ty), is_reftype(ty0), junkref(str, r, st), junkref(str, r0, st)

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, sk, 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, sk, sks)]]