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Proof step 62 from proof junkrefs-put-nopathex (previous step)

is_array(str, r1, st), junkrefs(str, r1 ' + acc, ty, st[r0 -- sk, val]), st[r1 -- _type] .type ≤ ty, ∀ str0, r2, st0, ty0, sk0, val0. ¬ path∃(str0, acc .first, r2, st0) ∧ ¬ junkrefs(str0, acc, ty0, st0) ∧ sk0 ≠ _type ∧ acc ≠ [] → ¬ junkrefs(str0, acc, ty0, st0[r2 -- sk0, val0]) ⊦ sk = _type, r1 = jvmref, junkrefs(str, r1 ' + acc, ty, st), path∃(str, r1, r0, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 34:
⊦ 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 38:
¬ (is_array(str, r1, st[r0 -- sk, val]) ∧ (st[r0 -- sk, val][r1 -- _type]) .type ≤ ty), is_array(str, r1, st), junkrefs(str, r1 ' + acc, ty, st[r0 -- sk, val]), st[r1 -- _type] .type ≤ ty, ∀ str0, r2, st0, ty0, sk0, val0. ¬ path∃(str0, acc .first, r2, st0) ∧ ¬ junkrefs(str0, acc, ty0, st0) ∧ sk0 ≠ _type ∧ acc ≠ [] → ¬ junkrefs(str0, acc, ty0, st0[r2 -- sk0, val0]) ⊦ sk = _type, r1 = jvmref, junkrefs(str, r1 ' + acc, ty, st), path∃(str, r1, r0, st)
Proof step 61:
is_array(str, r1, st[r0 -- sk, val]) ∧ (st[r0 -- sk, val][r1 -- _type]) .type ≤ ty, is_array(str, r1, st), acc ≠ [] ∧ (∃ i. 0 ≤ i ∧ i < (st[r0 -- sk, val][r1 -- _length]) .intval ∧ is_referencevalue(st[r0 -- sk, val][r1 -- i ']) ∧ acc .first = (st[r0 -- sk, val][r1 -- i ']) .refval ∧ junkrefs(str, acc, (st[r0 -- sk, val][r1 -- _type]) .type .type, st[r0 -- sk, val])), st[r1 -- _type] .type ≤ ty, ∀ str0, r2, st0, ty0, sk0, val0. ¬ path∃(str0, acc .first, r2, st0) ∧ ¬ junkrefs(str0, acc, ty0, st0) ∧ sk0 ≠ _type ∧ acc ≠ [] → ¬ junkrefs(str0, acc, ty0, st0[r2 -- sk0, val0]) ⊦ sk = _type, r1 = jvmref, junkrefs(str, r1 ' + acc, ty, 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[r0 -- sk, val], ty, acc, r1, str] ,F ,junkrefs , ,junkrefs-array ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st[r0 -- sk, val], ty, acc, r1, str)]]