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Proof step 40 from proof pathex-put-pathex-array-refval (previous step)

refs0 .first = (st[r0 -- i ', refval(r2)][r0 -- i0 ']) .refval, st[r0 -- _type] .type = mkarraytype(ty), is_referencevalue(st[r0 -- i ', refval(r2)][r0 -- i0 ']), i0 < st[r0 -- _length] .intval, is_array(str, r0, st[r0 -- i ', refval(r2)]), is_array(str, r0, st), i < st[r0 -- _length] .intval, validref(str, r2, ty, st), 0 < st[r0 -- _length] .intval, 0 ≤ i, 0 ≤ i0, validrefs(str, refs0, ty, st), r2 = jvmref → is_reftype(ty) ⊦ r0 = refs0 .last, r0 = jvmref, refs0 = [], path∃(str, r0, refs0 .last, st), path∃(str, r2, refs0 .last, st), r0 ∈ refs0, dups(refs0)

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, r, 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, r, refs)]]