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Proof step 54 from proof junkrefs-put-nopathex (previous step)

st[r1 -- i '] = refval(r2), 0 ≤ i, junkrefs(str, r2 ' + refs, st[r1 -- _type] .type .type, st[r0 -- sk, val]), i < st[r1 -- _length] .intval, st[r1 -- _type] .type ≤ ty, is_array(str, r1, st), 0 < st[r1 -- _length] .intval, ∀ str0, r, st0, ty0, sk0, val0. ¬ path∃(str0, r2, r, st0) ∧ ¬ junkrefs(str0, r2 ' + refs, ty0, st0) ∧ sk0 ≠ _type → ¬ junkrefs(str0, r2 ' + refs, ty0, st0[r -- sk0, val0]) ⊦ r1 = jvmref, sk = _type, r1 = r0, junkrefs(str, r1 ' + r2 ' + refs, ty, st), path∃(str, r1, r0, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 41:
⊦ is_array(str, r, st) ∧ st[r -- _type] .type ≤ ty → ( junkrefs(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 ∧ junkrefs(str, refs, st[r -- _type] .type .type, st)))
Proof step 53:
is_array(str, r1, st) ∧ st[r1 -- _type] .type ≤ ty, st[r1 -- i '] = refval(r2), 0 ≤ i, junkrefs(str, r2 ' + refs, st[r1 -- _type] .type .type, st[r0 -- sk, val]), i < st[r1 -- _length] .intval, st[r1 -- _type] .type ≤ ty, is_array(str, r1, st), 0 < st[r1 -- _length] .intval, ∀ str0, r, st0, ty0, sk0, val0. ¬ path∃(str0, r2, r, st0) ∧ ¬ junkrefs(str0, r2 ' + refs, ty0, st0) ∧ sk0 ≠ _type → ¬ junkrefs(str0, r2 ' + refs, ty0, st0[r -- sk0, val0]) ⊦ r1 = jvmref, sk = _type, r1 = r0, r2 ' + refs ≠ [] ∧ (∃ i. 0 ≤ i ∧ i < st[r1 -- _length] .intval ∧ is_referencevalue(st[r1 -- i ']) ∧ (r2 ' + refs) .first = st[r1 -- i '] .refval ∧ junkrefs(str, r2 ' + refs, st[r1 -- _type] .type .type, st)), path∃(str, r1, r0, st)

Rule argument

[speclemmaarg: , is_array(str, r, st) ∧ st[r -- _type] .type ≤ ty → ( junkrefs(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 ∧ junkrefs(str, refs, st[r -- _type] .type .type, st))) ,[st, ty, refs, r, str] → [st, ty, r2 ' + refs, r1, str] ,F ,junkrefs , ,junkrefs-array ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1])], [EXTRATERMS : (st, ty, r2 ' + refs, r1, str)]]