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Proof step 7 from proof pathex-array (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ path∃(str, r, r0, st) ↔ (∃ refs. refs ≠ [] ∧ refs .first = r ∧ refs .last = r0 ∧ validrefs(str, refs, st[r -- _type] .type, st))
Proof step 6:
validrefs(str, st[r -- i '] .refval ' + refs, st[r -- _type] .type .type, st), is_referencevalue(st[r -- i ']), i < st[r -- _length] .intval, is_array(str, r, st), 0 < st[r -- _length] .intval, 0 ≤ i, is_valid_ref(str, st[r -- i '] .refval, st), st[st[r -- i '] .refval -- _type] .type ≤ st[r -- _type] .type .type ⊦ r = (st[r -- i '] .refval ' + refs) .last, st[r -- i '] .refval = jvmref, ∃ refs0. refs0 ≠ [] ∧ refs0 .first = st[r -- i '] .refval ∧ refs0 .last = (st[r -- i '] .refval ' + refs) .last ∧ validrefs(str, refs0, st[st[r -- i '] .refval -- _type] .type, st)

Rule argument

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

Additional information

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