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Proof step 61 from proof junkrefs-put-null-01 (previous step)

st[r0 -- i '] = refval(r2), junkrefs (str, r2 ' + refs, (st[r -- mkfs(class, ty0, fieldvar) ', refval(jvmref)][r0 -- _type]) .type .type, st[r -- mkfs(class, ty0, fieldvar) ', refval(jvmref)]), 0 < (st[r -- mkfs(class, ty0, fieldvar) ', refval(jvmref)][r0 -- _length]) .intval, 0 ≤ i, i < (st[r -- mkfs(class, ty0, fieldvar) ', refval(jvmref)][r0 -- _length]) .intval, is_array(str, r0, st), (st[r -- mkfs(class, ty0, fieldvar) ', refval(jvmref)][r0 -- _type]) .type ≤ ty, is_array(str, r0, st[r -- mkfs(class, ty0, fieldvar) ', refval(jvmref)]), st[r0 -- _type] .type ≤ ty, is_reftype(ty0), ∀ str0, ty1, st0, fs, r1. ¬ junkrefs(str0, r2 ' + refs, ty1, st0) ∧ is_reftype(fs .type) → ¬ junkrefs(str0, r2 ' + refs, ty1, st0[r1 -- fs ', refval(jvmref)]), r0 ≠ r ∨ _type ≠ mkfs(class, ty0, fieldvar) ' ⊦ r0 = jvmref, junkrefs(str, r0 ' + r2 ' + refs, ty, st)

Heuristic weak cut applied rule cut formula

And obtained the following new goals

Proof step 60:
st[r0 -- i '] = refval(r2), junkrefs (str, r2 ' + refs, (st[r -- mkfs(class, ty0, fieldvar) ', refval(jvmref)][r0 -- _type]) .type .type, st[r -- mkfs(class, ty0, fieldvar) ', refval(jvmref)]), 0 < (st[r -- mkfs(class, ty0, fieldvar) ', refval(jvmref)][r0 -- _length]) .intval, 0 ≤ i, i < (st[r -- mkfs(class, ty0, fieldvar) ', refval(jvmref)][r0 -- _length]) .intval, is_array(str, r0, st), (st[r -- mkfs(class, ty0, fieldvar) ', refval(jvmref)][r0 -- _type]) .type ≤ ty, is_array(str, r0, st[r -- mkfs(class, ty0, fieldvar) ', refval(jvmref)]), st[r0 -- _type] .type ≤ ty, is_reftype(ty0), ∀ str0, ty1, st0, fs, r1. ¬ junkrefs(str0, r2 ' + refs, ty1, st0) ∧ is_reftype(fs .type) → ¬ junkrefs(str0, r2 ' + refs, ty1, st0[r1 -- fs ', refval(jvmref)]), r0 ≠ r ∨ _type ≠ mkfs(class, ty0, fieldvar) ' ⊦ r0 -- _length = r -- mkfs(class, ty0, fieldvar) ', r0 = jvmref, junkrefs(str, r0 ' + r2 ' + refs, ty, st)

Rule argument

[fma-arg: r0 -- _length = r -- mkfs(class, ty0, fieldvar) ']

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ r -- sk = r0 -- sk0 ↔ r = r0 ∧ sk = sk0], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ sk ≠ sk0 → (st[r -- sk, val][r0 -- sk0]) = st[r0 -- sk0]], [CSIMPFORWARD : ⊦ mkfs(class1, ty, fieldvar) ' = _length → class1 = `*Array*' .class ∧ ty = int_type ∧ fieldvar = `length' .field], [CSIMPFORWARD : ⊦ i < j ∧ 0 ≤ i → 0 < j], [CSIMPSEQ : ⊦ mkfs (`*Array*' .class, int_type, `length' .field) ' = _length], [CSIMPSEQ : ⊦ _type ≠ _length], [CSIMPSEQ : ⊦ (st[rk, val][rk]) = val], [CSIMPSEQ : ⊦ ¬ is_reftype(int_type)])], [EXTRAFMAS : (r0 -- _length = r -- mkfs(class, ty0, fieldvar) ')]]