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Proof step 116 from proof pathex-put-pathex-array-refval (previous step)

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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 115:
refs = r + refs0, st[r0 -- _type] .type = mkarraytype(ty), 0 ≤ i, 0 < st[r0 -- _length] .intval, validref(str, r2, ty, st), i < st[r0 -- _length] .intval, path∃(str, r, r0, st), validrefs(str, refs, st[r -- _type] .type, st[r0 -- i ', refval(r2)]), r2 = jvmref → is_reftype(ty) ⊦ r0 = jvmref, refs = [], r = refs .last, path∃(str, r2, refs .last, st), path∃(str, r, refs .last, st), dups(refs)

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] → [refs, r, refs0] 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 : (refs, r, refs0)]]