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Proof step 60 from proof junkref-update-equiv (previous step)

junkrefs(str, refs, st[refs .first -- _type] .type, st), validFields(r0, fis, st), is_valid_ref(str, r0, st) ⊦ refs = [], junkref(str, refs .first, update(r0, fis, st)), path∃(str, refs .first, r0, st), _type ∈ fis

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 59:
refs = r + refs0, junkrefs(str, refs, st[r -- _type] .type, st), validFields(r0, fis, st), is_valid_ref(str, r0, st) ⊦ refs = [], junkref(str, r, update(r0, fis, st)), path∃(str, r, r0, st), _type ∈ fis

Rule argument

[speclemmaarg: refs ≠ [] ,r = refs .first ∧ refs0 = refs .rest ↔ refs = r + refs0 ,[refs, r, refs0] → [refs, r, refs0] ,T ,list-data ,references-olista ,elim-list-c ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : refs ≠ [] ⊦ r = refs .first ∧ refs0 = refs .rest ↔ refs = r + refs0])], [EXTRATERMS : (refs, r, refs0)]]