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Proof step 20 from proof unchNorec-validrefs (previous step)

st[r -- _type] = st0[r -- _type], refs0 .first = st[r -- mkfs(class, ty0, fieldvar) '] .refval, is_obj(str, r, st0), is_obj(str, r, st), st0[r -- _type] .type ≤ ty, unchangedNorec(r, st, st0), mkfs(class, ty0, fieldvar) ' ∈ instfields(st0[r -- _type] .type .class), is_referencevalue(st[r -- mkfs(class, ty0, fieldvar) ']), validrefs(str, refs0, ty0, st), ∀ str, ty, st, st0. validrefs(str, refs0, ty, st) ∧ (∀ r. r ∈ refs0 → unchangedNorec(r, st, st0)) → validrefs(str, refs0, ty, st0), ∀ r0. r0 ∈ refs0 → unchangedNorec(r0, st, st0) ⊦ r = jvmref, refs0 = [], ∃ fs. fs ' ∈ instfields(st0[r -- _type] .type .class) ∧ is_referencevalue(st0[r -- fs ']) ∧ refs0 .first = st0[r -- fs '] .refval ∧ validrefs(str, refs0, fs .type, st0)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Rule argument

[x0lemmaarg: spec-name: list-data instance-name: references lemma-name: elim-list-c antecedent: refs ≠ [] succedent: r = refs .first ∧ refs0 = refs .rest ↔ refs = r + refs0 substlist: [refs, r, refs0] → [refs0, r1, refs] add preconditions?: F is rewrite lemma?: F current spec?: F rotate lemma?: T replace all?: T paths: () dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : refs ≠ [] ⊦ r = refs .first ∧ refs0 = refs .rest ↔ refs = r + refs0])], [EXTRATERMS : (refs0, r1, refs)]]