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Proof step 26 from proof validrefs-postfix (previous step)

is_array(str, r, st), validrefs(str, r ' + acc + r0 ' + refs, ty, st), st[r -- _type] .type ≤ ty, ∀ str, refs0, st, ty. ¬ validrefs(str, refs0, st[refs0 .first -- _type] .type, st) ∧ refs0 ≠ [] → ¬ validrefs(str, acc + refs0, ty, st) ⊦ r = jvmref, validrefs(str, r0 ' + refs, st[r0 -- _type] .type, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 18:
⊦ is_array(str, r, st) ∧ st[r -- _type] .type ≤ ty → ( validrefs(str, r ' + refs, ty, st) ↔ refs = [] ∨ (∃ i. 0 ≤ i ∧ i < st[r -- _length] .intval ∧ is_referencevalue(st[r -- i ']) ∧ refs .first = st[r -- i '] .refval ∧ validrefs(str, refs, st[r -- _type] .type .type, st)))
Proof step 25:
is_array(str, r, st) ∧ st[r -- _type] .type ≤ ty, is_array(str, r, st), acc + r0 ' + refs = [] ∨ (∃ i. 0 ≤ i ∧ i < st[r -- _length] .intval ∧ is_referencevalue(st[r -- i ']) ∧ (acc + r0 ' + refs) .first = st[r -- i '] .refval ∧ validrefs(str, acc + r0 ' + refs, st[r -- _type] .type .type, st)), st[r -- _type] .type ≤ ty, ∀ str, refs0, st, ty. ¬ validrefs(str, refs0, st[refs0 .first -- _type] .type, st) ∧ refs0 ≠ [] → ¬ validrefs(str, acc + refs0, ty, st) ⊦ r = jvmref, validrefs(str, r0 ' + refs, st[r0 -- _type] .type, st)

Rule argument

[crewrite-arg: validrefs-array , F , [st, ty, refs, r, str] → [st, ty, acc + r0 ' + refs, r, str] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, ty, acc + r0 ' + refs, r, str)]]