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Proof step 30 from proof validrefs-prefix (previous step)

is_array(str, r, st), st[r -- _type] .type ≤ ty, ∀ str, refs0, ty, st. validrefs(str, acc + refs0, ty, st) → validrefs(str, acc, ty, st), acc = [] ∧ refs0 = [] ∨ 0 ≤ i ∧ i < st[r -- _length] .intval ∧ is_referencevalue(st[r -- i ']) ∧ (acc + refs0) .first = st[r -- i '] .refval ∧ validrefs(str, acc + refs0, st[r -- _type] .type .type, st) ⊦ r = jvmref, validrefs(str, r ' + acc, ty, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 21:
⊦ 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 29:
is_array(str, r, st) ∧ st[r -- _type] .type ≤ ty, is_array(str, r, st), st[r -- _type] .type ≤ ty, ∀ str, refs0, ty, st. validrefs(str, acc + refs0, ty, st) → validrefs(str, acc, ty, st), acc = [] ∧ refs0 = [] ∨ 0 ≤ i ∧ i < st[r -- _length] .intval ∧ is_referencevalue(st[r -- i ']) ∧ (acc + refs0) .first = st[r -- i '] .refval ∧ validrefs(str, acc + refs0, st[r -- _type] .type .type, st) ⊦ r = jvmref, acc = [] ∨ (∃ i. 0 ≤ i ∧ i < st[r -- _length] .intval ∧ is_referencevalue(st[r -- i ']) ∧ acc .first = st[r -- i '] .refval ∧ validrefs(str, acc, st[r -- _type] .type .type, st))

Rule argument

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

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, ty, acc, r, str)]]