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Proof step 55 from proof junkrefs-put-nopathex (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 40:
⊦ path∃(str, r, r, st) ↔ r = jvmref ∨ r ≠ jvmref ∧ is_valid_ref(str, r, st)
Proof step 54:
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)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPFORWARD : ⊦ i < j ∧ 0 ≤ i → 0 < j], [CSIMPSEQ : ⊦ r ≠ r0 → ( is_array (str, r0, st[r -- sk, val]) ↔ is_array(str, r0, st))], [CSIMPSEQ : ⊦ r ≠ r0 → (st[r0 -- sk0, val][r -- sk]) = st[r -- sk]], [CSIMPSEQ : ⊦ is_array(str, r, st) → is_valid_ref(str, r, st)], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ r -- sk = r0 -- sk0 ↔ ¬ ¬ (r = r0 ∧ sk = sk0)])]]