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Proof step 45 from proof unchNorec-validrefs (previous step)

refs0 .first = st[r -- i '] .refval, st0[r -- _type] .type = mkarraytype(ty0), st[r -- _type] = st0[r -- _type], st[r -- _length] = st0[r -- _length], 0 < st0[r -- _length] .intval, 0 ≤ i, validrefs(str, refs0, ty0, st), is_referencevalue(st[r -- i ']), i < st0[r -- _length] .intval, is_array(str, r, st), unchangedNorec(r, st, st0), mkarraytype(ty0) ≤ ty, is_array(str, r, st0), ∀ 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) ⊦ refs0 = [], r = jvmref, ∃ i0. ¬ i0 < 0 ∧ ¬ st0[r -- _length] .intval ≤ i0 ∧ is_referencevalue(st0[r -- i0 ']) ∧ refs0 .first = st0[r -- i0 '] .refval ∧ validrefs(str, refs0, ty0, 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)]]