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Proof step 48 from proof pathex-array (previous step)

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

User applied rule insert elim lemma

And obtained the following new goals

Proof step 47:
refs = r0 + refs0, r0 = st[r -- i '] .refval, is_referencevalue(st[r -- i ']), is_array(str, r, st), i < st[r -- _length] .intval, 0 ≤ i, 0 < st[r -- _length] .intval, st[r0 -- _type] .type ≤ st[r -- _type] .type .type, validrefs(str, refs, st[r0 -- _type] .type, st) ⊦ r = refs .last, r0 = jvmref, refs = [], path∃(str, r, refs .last, st)

Rule argument

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

Additional information

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