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Proof step 177 from proof pathex-put-nopathex (previous step)

st[r -- i '] = refval(r1), 0 ≤ i, 0 < st[r -- _length] .intval, is_array(str, r, st), i < st[r -- _length] .intval, validrefs(str, r1 ' + refs1, st[r -- _type] .type .type, st), path∃(str, r1, r0, st) ∨ junkref(str, r1, st) ∨ path∃(str, r1, (r1 ' + refs1) .last, st[r0 -- sk, val]), ∀ val, r0, sk, st0, r2, str, refs. # refs < # (r1 + refs1) → ( validrefs(str, r2 ' + refs, st0[r2 -- _type] .type, st0) → sk = _type ∨ path∃(str, r2, r0, st0) ∨ junkref(str, r2, st0) ∨ path∃(str, r2, (r2 ' + refs) .last, st0[r0 -- sk, val])) ⊦ r = r0, sk = _type, r = jvmref, r = (r1 ' + refs1) .last, r1 = jvmref ∧ (jvmref ' + refs1) .last = jvmref, r1 ≠ jvmref ∧ st[r1 -- _type] .type ≤ st[r -- _type] .type .type ∧ path∃(str, r1, (r1 ' + refs1) .last, st[r0 -- sk, val]), r1 ≠ jvmref ∧ (¬ st[r1 -- _type] .type ≤ st[r -- _type] .type .type ∨ junkref(str, r1, st)), r1 ≠ jvmref ∧ st[r1 -- _type] .type ≤ st[r -- _type] .type .type ∧ path∃(str, r1, r0, st), r1 = jvmref ∧ r0 = jvmref

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 172:
⊦ r ≠ jvmref ∧ (¬ is_valid_ref(str, r, st) ∨ ¬ st[r -- _type] .type ≤ ty) → ¬ validrefs(str, r ' + refs, ty, st)
Proof step 176:
¬ (r1 ≠ jvmref ∧ (¬ is_valid_ref(str, r1, st) ∨ ¬ st[r1 -- _type] .type ≤ st[r -- _type] .type .type)), st[r -- i '] = refval(r1), 0 ≤ i, 0 < st[r -- _length] .intval, is_array(str, r, st), i < st[r -- _length] .intval, validrefs(str, r1 ' + refs1, st[r -- _type] .type .type, st), path∃(str, r1, r0, st) ∨ junkref(str, r1, st) ∨ path∃(str, r1, (r1 ' + refs1) .last, st[r0 -- sk, val]), ∀ val, r0, sk, st0, r2, str, refs. # refs < # (r1 + refs1) → ( validrefs(str, r2 ' + refs, st0[r2 -- _type] .type, st0) → sk = _type ∨ path∃(str, r2, r0, st0) ∨ junkref(str, r2, st0) ∨ path∃(str, r2, (r2 ' + refs) .last, st0[r0 -- sk, val])) ⊦ r = r0, sk = _type, r = jvmref, r = (r1 ' + refs1) .last, r1 = jvmref ∧ (jvmref ' + refs1) .last = jvmref, r1 ≠ jvmref ∧ st[r1 -- _type] .type ≤ st[r -- _type] .type .type ∧ path∃(str, r1, (r1 ' + refs1) .last, st[r0 -- sk, val]), r1 ≠ jvmref ∧ (¬ st[r1 -- _type] .type ≤ st[r -- _type] .type .type ∨ junkref(str, r1, st)), r1 ≠ jvmref ∧ st[r1 -- _type] .type ≤ st[r -- _type] .type .type ∧ path∃(str, r1, r0, st), r1 = jvmref ∧ r0 = jvmref

Rule argument

[crewrite-arg: validrefs-is-junk , F , [st, ty, refs, r, str] → [st, st[r -- _type] .type .type, refs1, r1, str] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, st[r -- _type] .type .type, refs1, r1, str)]]