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Proof step 38 from proof junkrefs-put-nopathex-equiv (previous step)

st[r1 -- i '] = refval(r2), st[r1 -- _type] .type ≤ ty, is_array(str, r1, st), 0 ≤ i, 0 < st[r1 -- _length] .intval, is_valid_ref(str, r0, st), i < st[r1 -- _length] .intval, junkrefs(str, r2 ' + refs, st[r1 -- _type] .type .type, st), path∃(str, r2, r0, st) ⊦ r0 = r1, r1 = jvmref, sk = _type, path∃(str, r1, r0, st), junkrefs(str, r2 ' + refs, st[r1 -- _type] .type .type, st[r0 -- sk, val])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 32:
⊦ is_array(str, r, st) ∧ r ≠ r0 → ( path∃(str, r, r0, st) ↔ (∃ i. 0 ≤ i ∧ i < st[r -- _length] .intval ∧ is_referencevalue(st[r -- i ']) ∧ ( st[r -- i '] .refval ≠ jvmref ∧ st[st[r -- i '] .refval -- _type] .type ≤ st[r -- _type] .type .type ∧ path∃(str, st[r -- i '] .refval, r0, st) ∨ st[r -- i '] .refval = jvmref ∧ r0 = jvmref)))
Proof step 37:
is_array(str, r1, st) ∧ r1 ≠ r0, st[r1 -- i '] = refval(r2), st[r1 -- _type] .type ≤ ty, is_array(str, r1, st), 0 ≤ i, 0 < st[r1 -- _length] .intval, is_valid_ref(str, r0, st), i < st[r1 -- _length] .intval, junkrefs(str, r2 ' + refs, st[r1 -- _type] .type .type, st), path∃(str, r2, r0, st) ⊦ r0 = r1, r1 = jvmref, sk = _type, ∃ i. 0 ≤ i ∧ i < st[r1 -- _length] .intval ∧ is_referencevalue(st[r1 -- i ']) ∧ ( st[r1 -- i '] .refval ≠ jvmref ∧ st[st[r1 -- i '] .refval -- _type] .type ≤ st[r1 -- _type] .type .type ∧ path∃(str, st[r1 -- i '] .refval, r0, st) ∨ st[r1 -- i '] .refval = jvmref ∧ r0 = jvmref), junkrefs(str, r2 ' + refs, st[r1 -- _type] .type .type, st[r0 -- sk, val])

Rule argument

[crewrite-arg: pathex-array, F, [st, r0, r, str] → [st, r0, r1, str]]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1])], [EXTRATERMS : (st, r0, r1, str)]]