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Proof step 24 from proof validrefs-not-in-01 (previous step)

is_array(str, r0, st), r ∈ acc, validrefs(str, r0 ' + acc, ty, st), st[r0 -- _type] .type ≤ ty, ∀ r, str, ty, st. r ∈ acc ∧ validrefs(str, acc, ty, st) → r = jvmref ∨ is_valid_ref(str, r, st) ⊦ r0 = jvmref, r = r0, r = jvmref, is_valid_ref(str, r, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 16:
⊦ 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 23:
is_array(str, r0, st) ∧ st[r0 -- _type] .type ≤ ty, is_array(str, r0, st), r ∈ acc, acc = [] ∨ (∃ i. 0 ≤ i ∧ i < st[r0 -- _length] .intval ∧ is_referencevalue(st[r0 -- i ']) ∧ acc .first = st[r0 -- i '] .refval ∧ validrefs(str, acc, st[r0 -- _type] .type .type, st)), st[r0 -- _type] .type ≤ ty, ∀ r, str, ty, st. r ∈ acc ∧ validrefs(str, acc, ty, st) → r = jvmref ∨ is_valid_ref(str, r, st) ⊦ r0 = jvmref, r = r0, r = jvmref, is_valid_ref(str, r, st)

Rule argument

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

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, ty, acc, r0, str)]]