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Proof step 9 from proof pathex-junkref (previous step)

refs .first = refs0 .last, junkrefs(str, refs, st[refs0 .last -- _type] .type, st), validrefs(str, r ' + refs0, st[r -- _type] .type, st) ⊦ refs = [], refs0 = [], ∃ refs. refs ≠ [] ∧ refs .first = r ∧ junkrefs(str, refs, st[refs .first -- _type] .type, st)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 8:
refs = r0 + refs1, r0 = refs0 .last, junkrefs(str, refs, st[refs0 .last -- _type] .type, st), validrefs(str, r ' + refs0, st[r -- _type] .type, st) ⊦ refs = [], refs0 = [], ∃ refs. refs ≠ [] ∧ refs .first = r ∧ junkrefs(str, refs, st[refs .first -- _type] .type, st)

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, r0, 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 : (refs, r0, refs1)]]