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Proof step 41 from proof junkrefs-put-nopathex-equiv (previous step)

st[r1 -- i '] = refval(r2), junkrefs(str, r2 ' + refs, st[r1 -- _type] .type .type, st), i < st[r1 -- _length] .intval, is_valid_ref(str, r0, st), 0 < st[r1 -- _length] .intval, 0 ≤ i, is_array(str, r1, st), st[r1 -- _type] .type ≤ ty, ∀ str0, r, st0, sk0, ty0, val0. ¬ path∃(str0, r2, r, st0) ∧ is_valid_ref(str0, r, st0) ∧ sk0 ≠ _type → (junkrefs(str0, r2 ' + refs, ty0, st0[r -- sk0, val0]) ↔ junkrefs(str0, r2 ' + refs, ty0, st0)) ⊦ sk = _type, r1 = jvmref, r0 = r1, path∃(str, r1, r0, st), ¬ i < 0 ∧ ¬ st[r1 -- _length] .intval ≤ i ∧ is_referencevalue(st[r1 -- i ']) ∧ r2 = st[r1 -- i '] .refval ∧ junkrefs(str, st[r1 -- i '] .refval ' + refs, st[r1 -- _type] .type .type, st[r0 -- sk, val])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 40:
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), ∀ str0, r, st0, sk0, ty0, val0. ¬ path∃(str0, r2, r, st0) ∧ is_valid_ref(str0, r, st0) ∧ sk0 ≠ _type → (junkrefs(str0, r2 ' + refs, ty0, st0[r -- sk0, val0]) ↔ junkrefs(str0, r2 ' + refs, ty0, st0)) ⊦ r0 = r1, r1 = jvmref, sk = _type, path∃(str, r1, r0, st), junkrefs(str, r2 ' + refs, st[r1 -- _type] .type .type, st[r0 -- sk, val])

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ refval(r) .refval = r], [CSIMPSEQ : ⊦ is_referencevalue(refval(r))], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ i < j → (¬ ¬ j ≤ i ↔ false)], [CSIMPSEQ : ⊦ i ≤ j → (¬ ¬ j < i ↔ false)])]]