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Proof step 69 from proof disjoint-nojunk-newref-subset-01 (previous step)

refs0 .last = refs .last, validrefs(str, refs0, st1[refs0 .first -- _type] .type, st1), validrefs(str, refs, st1[refs .first -- _type] .type, st1), st ⊆ st1, newref(r, st), ∀ r0. path∃(str, r, r0, st1) → newref(r0, st) ∨ r0 = jvmref ⊦ r = jvmref, refs .last = jvmref, refs0 .first = refs .first, refs = [], refs0 = [], junkref(str, r1, st), refs0 .first ≠ r1 ∧ refs0 .first ≠ r, refs .first ≠ r1 ∧ refs .first ≠ r

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 68:
refs0 = r2 + refs1, refs0 .last = refs .last, validrefs(str, refs0, st1[r2 -- _type] .type, st1), validrefs(str, refs, st1[refs .first -- _type] .type, st1), st ⊆ st1, newref(r, st), ∀ r0. path∃(str, r, r0, st1) → newref(r0, st) ∨ r0 = jvmref ⊦ r = jvmref, refs .last = jvmref, r2 = refs .first, refs = [], refs0 = [], junkref(str, r1, st), r2 ≠ r1 ∧ r2 ≠ r, refs .first ≠ r1 ∧ refs .first ≠ r

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, r2, refs1] 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, r2, refs1)]]