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Proof step 46 from proof pathex-array (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 35:
⊦ path∃(str, r, r0, st) ↔ (∃ refs. refs ≠ [] ∧ refs .first = r ∧ refs .last = r0 ∧ validrefs(str, refs, st[r -- _type] .type, st))
Proof step 45:
is_referencevalue(st[r -- i ']), is_array(str, r, st), i < st[r -- _length] .intval, 0 ≤ i, 0 < st[r -- _length] .intval, st[st[r -- i '] .refval -- _type] .type ≤ st[r -- _type] .type .type, validrefs(str, st[r -- i '] .refval ' + refs0, st[st[r -- i '] .refval -- _type] .type, st) ⊦ st[r -- i '] .refval = jvmref, r = (st[r -- i '] .refval ' + refs0) .last, ∃ refs. refs ≠ [] ∧ refs .first = r ∧ refs .last = (st[r -- i '] .refval ' + refs0) .last ∧ validrefs(str, refs, st[r -- _type] .type, st)

Rule argument

[crewrite-arg: pathex-def-simple , F , [st, r0, r, str] → [st, (st[r -- i '] .refval ' + refs0) .last, r, str] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, (st[r -- i '] .refval ' + refs0) .last, r, str)]]