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Proof step 147 from proof validrefs-not-contains (previous step)

validrefs(str, r ' + r0 ' + refs, ty, st), ∀ str0, st0, ty0. ¬ contains(str0, st0[r0 -- _type] .type, st0[refs .last -- _type] .type) ∧ r0 ≠ refs .last → ¬ validrefs(str0, r0 ' + refs, ty0, st0) ⊦ refs = [], refs .last = jvmref, r = refs .last, contains(str, st[r -- _type] .type, st[refs .last -- _type] .type)

User applied rule insert elim lemma

And obtained the following new goals

Proof step 146:
refs = refs0 + r1 ', validrefs(str, r ' + r0 ' + refs, ty, st), ∀ str0, st0, ty0. ¬ contains(str0, st0[r0 -- _type] .type, st0[r1 -- _type] .type) ∧ r0 ≠ r1 → ¬ validrefs(str0, r0 ' + refs, ty0, st0) ⊦ refs = [], r1 = jvmref, r = r1, contains(str, st[r -- _type] .type, st[r1 -- _type] .type)

Rule argument

[speclemmaarg: refs ≠ [] ,r = refs .last ∧ refs0 = refs .butlast ↔ refs = refs0 + r ' ,[refs, r, refs0] → [refs, r1, refs0] ,T ,list-last ,references-olista ,last-elim ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : refs ≠ [] ⊦ r = refs .last ∧ refs0 = refs .butlast ↔ refs = refs0 + r '])], [EXTRATERMS : (refs, r1, refs0)]]