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Proof step 14 from proof pathex-array (previous step)

refs0 .first = st[r -- i '] .refval, is_array(str, r, st), i < st[r -- _length] .intval, is_referencevalue(st[r -- i ']), validrefs(str, refs0, st[r -- _type] .type .type, st), 0 ≤ i, 0 < st[r -- _length] .intval ⊦ refs0 = [], r = refs0 .last, refs0 .first ≠ jvmref ∧ st[refs0 .first -- _type] .type ≤ st[r -- _type] .type .type ∧ path∃(str, refs0 .first, refs0 .last, st), refs0 .first = jvmref ∧ refs0 .last = jvmref

User applied rule insert elim lemma

And obtained the following new goals

Proof step 13:
refs0 = r0 + refs, r0 = st[r -- i '] .refval, is_array(str, r, st), i < st[r -- _length] .intval, is_referencevalue(st[r -- i ']), validrefs(str, refs0, st[r -- _type] .type .type, st), 0 ≤ i, 0 < st[r -- _length] .intval ⊦ refs0 = [], r = refs0 .last, r0 ≠ jvmref ∧ st[r0 -- _type] .type ≤ st[r -- _type] .type .type ∧ path∃(str, r0, refs0 .last, st), r0 = jvmref ∧ refs0 .last = jvmref

Rule argument

[speclemmaarg: ,refs ≠ [] → (r = refs .first ∧ refs0 = refs .rest ↔ refs = r + refs0) ,[refs, r, refs0] → [refs0, r0, refs] ,T ,list-data ,references-olista ,elim-1 ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : ⊦ refs ≠ [] → ( r = refs .first ∧ refs0 = refs .rest ↔ refs = r + refs0)])], [EXTRATERMS : (refs0, r0, refs)]]