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Proof step 2 from proof validrefs-postfix (previous step)

validrefs(str, refs0, ty, st) ⊦ refs0 = [], validrefs(str, refs0, st[refs0 .first -- _type] .type, st)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 1:
⊦ ¬ validrefs(str, r ' + refs, st[r -- _type] .type, st) → ¬ validrefs(str, r ' + refs, ty, st)

Rule argument

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

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ r + refs = r ' + refs], [CSIMPSEQ : ⊦ r ' + refs ≠ []], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPELIM : refs ≠ [] ⊦ r = refs .first ∧ refs0 = refs .rest ↔ refs = r + refs0])], [EXTRATERMS : (refs0, r, refs)]]