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Proof step 41 from proof validrefs-junkrefs-append (previous step)

refs .last = refs0 .first, junkrefs(str, refs0, st[refs0 .first -- _type] .type, st), validrefs(str, refs, ty, st) ⊦ refs0 = [], refs = [], junkrefs(str, refs + refs0 .rest, ty, st)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 40:
refs0 = r + refs1, refs .last = r, junkrefs(str, refs0, st[r -- _type] .type, st), validrefs(str, refs, ty, st) ⊦ refs0 = [], refs = [], junkrefs(str, refs + refs1, ty, 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] → [refs0, r, 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, r, refs1)]]