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Proof step 98 from proof junkrefs-put-nopathexplus-equiv (previous step)

st[r -- i '] = refval(r1), junkrefs(str, r1 ' + refs1, st[r -- _type] .type .type, st), i < st[r -- _length] .intval, 0 < st[r -- _length] .intval, 0 ≤ i, is_array(str, r, st), st[r -- _type] .type ≤ ty, r1 = r0 ∨ refs ≠ [] ∧ refs .first = r1 ∧ validrefs(str, refs, mkclasstype(`java.lang.Object' .class), st) ∧ step∃(str, refs .last, r0, st), ∀ val, sk, r0, st0, ty, r2, str, refs. # refs < # (r1 + refs1) → (junkrefs(str, r2 ' + refs, ty, st0) → junkrefs(str, r2 ' + refs, ty, st0[r0 -- sk, val]) ∨ sk = _type ∨ path∃+(str, r2, r0, st0)) ⊦ r = r0, sk = _type, r = jvmref, junkrefs(str, r1 ' + refs1, st[r -- _type] .type .type, st[r0 -- sk, val]), ∃ refs. refs ≠ [] ∧ refs .first = r ∧ validrefs(str, refs, mkclasstype(`java.lang.Object' .class), st) ∧ step∃(str, refs .last, r0, st)

User applied rule cut formula

And obtained the following new goals

Proof step 81:
r1 = r0, st[r -- i '] = refval(r1), junkrefs(str, r1 ' + refs1, st[r -- _type] .type .type, st), i < st[r -- _length] .intval, 0 < st[r -- _length] .intval, 0 ≤ i, is_array(str, r, st), st[r -- _type] .type ≤ ty, r1 = r0 ∨ refs ≠ [] ∧ refs .first = r1 ∧ validrefs(str, refs, mkclasstype(`java.lang.Object' .class), st) ∧ step∃(str, refs .last, r0, st), ∀ val, sk, r0, st0, ty, r2, str, refs. # refs < # (r1 + refs1) → (junkrefs(str, r2 ' + refs, ty, st0) → junkrefs(str, r2 ' + refs, ty, st0[r0 -- sk, val]) ∨ sk = _type ∨ path∃+(str, r2, r0, st0)) ⊦ r = r0, sk = _type, r = jvmref, junkrefs(str, r1 ' + refs1, st[r -- _type] .type .type, st[r0 -- sk, val]), ∃ refs. refs ≠ [] ∧ refs .first = r ∧ validrefs(str, refs, mkclasstype(`java.lang.Object' .class), st) ∧ step∃(str, refs .last, r0, st)
Proof step 97:
st[r -- i '] = refval(r1), junkrefs(str, r1 ' + refs1, st[r -- _type] .type .type, st), i < st[r -- _length] .intval, 0 < st[r -- _length] .intval, 0 ≤ i, is_array(str, r, st), st[r -- _type] .type ≤ ty, r1 = r0 ∨ refs ≠ [] ∧ refs .first = r1 ∧ validrefs(str, refs, mkclasstype(`java.lang.Object' .class), st) ∧ step∃(str, refs .last, r0, st), ∀ val, sk, r0, st0, ty, r2, str, refs. # refs < # (r1 + refs1) → (junkrefs(str, r2 ' + refs, ty, st0) → junkrefs(str, r2 ' + refs, ty, st0[r0 -- sk, val]) ∨ sk = _type ∨ path∃+(str, r2, r0, st0)) ⊦ r1 = r0, r = r0, sk = _type, r = jvmref, junkrefs(str, r1 ' + refs1, st[r -- _type] .type .type, st[r0 -- sk, val]), ∃ refs. refs ≠ [] ∧ refs .first = r ∧ validrefs(str, refs, mkclasstype(`java.lang.Object' .class), st) ∧ step∃(str, refs .last, r0, st)

Rule argument

[fma-arg: r1 = r0]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRAFMAS : (r1 = r0)]]