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Proof step 180 from proof pathex-put-nopathex (previous step)

is_array(str, r, st) ∧ r ≠ r0, st[r -- i '] = refval(r1), validrefs(str, r1 ' + refs1, st[r -- _type] .type .type, st), i < st[r -- _length] .intval, is_array(str, r, st), 0 < st[r -- _length] .intval, 0 ≤ i, 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, r = (r1 ' + refs1) .last, r = jvmref, sk = _type, ∃ 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), 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, (r1 ' + refs1) .last, st[r0 -- sk, val]), r1 = jvmref ∧ (jvmref ' + refs1) .last = jvmref

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 179:
st[r -- i '] = refval(r1), validrefs(str, r1 ' + refs1, st[r -- _type] .type .type, st), i < st[r -- _length] .intval, is_array(str, r, st), 0 < st[r -- _length] .intval, 0 ≤ i, 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 = (r1 ' + refs1) .last, r = jvmref, sk = _type, r = r0, 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, (r1 ' + refs1) .last, st[r0 -- sk, val]), r1 = jvmref ∧ (jvmref ' + refs1) .last = jvmref, ∃ i0. ¬ i0 < 0 ∧ ¬ st[r -- _length] .intval ≤ i0 ∧ is_referencevalue(st[r -- i0 ']) ∧ ( st[r -- i0 '] .refval ≠ jvmref ∧ st[st[r -- i0 '] .refval -- _type] .type ≤ st[r -- _type] .type .type ∧ path∃(str, st[r -- i0 '] .refval, r0, st) ∨ st[r -- i0 '] .refval = jvmref ∧ r0 = jvmref)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i])]]