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Proof step 43 from proof validrefs-junkrefs-01 (previous step)

st[r -- i '] = refval(r0), st[r -- _type] .type ≤ ty, 0 ≤ i, 0 < st[r -- _length] .intval, is_array(str, r, st), i < st[r -- _length] .intval, junkrefs(str, (r0 ' + refs1) + refs0, st[r -- _type] .type .type, st), ∀ str0, refs2, ty0, st0. junkrefs(str0, (r0 ' + refs1) + refs2, ty0, st0) → junkrefs(str0, r0 ' + refs1, ty0, st0) ∨ validrefs(str0, r0 ' + refs1, ty0, st0) ⊦ r = jvmref, validrefs(str, r ' + r0 ' + refs1, ty, st), junkrefs(str, r0 ' + refs1, st[r -- _type] .type .type, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 38:
⊦ 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 42:
is_array(str, r, st) ∧ st[r -- _type] .type ≤ ty, st[r -- i '] = refval(r0), st[r -- _type] .type ≤ ty, 0 ≤ i, 0 < st[r -- _length] .intval, is_array(str, r, st), i < st[r -- _length] .intval, junkrefs(str, (r0 ' + refs1) + refs0, st[r -- _type] .type .type, st), ∀ str0, refs2, ty0, st0. junkrefs(str0, (r0 ' + refs1) + refs2, ty0, st0) → junkrefs(str0, r0 ' + refs1, ty0, st0) ∨ validrefs(str0, r0 ' + refs1, ty0, st0) ⊦ r = jvmref, r0 ' + refs1 = [] ∨ (∃ i. 0 ≤ i ∧ i < st[r -- _length] .intval ∧ is_referencevalue(st[r -- i ']) ∧ (r0 ' + refs1) .first = st[r -- i '] .refval ∧ validrefs(str, r0 ' + refs1, st[r -- _type] .type .type, st)), junkrefs(str, r0 ' + refs1, st[r -- _type] .type .type, st)

Rule argument

[crewrite-arg: validrefs-array , F , [st, ty, refs, r, str] → [st, ty, r0 ' + refs1, r, str] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, ty, r0 ' + refs1, r, str)]]