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Proof step 40 from proof junkrefs-put-null (previous step)

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

Heuristic weak cut applied rule cut formula

And closed the goal!

Rule argument

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

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ i < j → (¬ ¬ j ≤ i ↔ false)], [CSIMPSEQ : ⊦ r ≠ r0 → (st[r0 -- sk0, val][r -- sk]) = st[r -- sk]], [CSIMPSEQ : ⊦ r ≠ r0 → ( is_array (str, r0, st[r -- sk, val]) ↔ is_array(str, r0, st))], [CSIMPSEQ : ⊦ r -- sk = r0 -- sk0 ↔ ¬ ¬ (r = r0 ∧ sk = sk0)], [CSIMPSEQ : ⊦ r -- sk = r0 -- sk0 ↔ r = r0 ∧ sk = sk0], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPFORWARD : ⊦ _type = mkfs(class1, ty, fieldvar) ' → class1 = `java.lang.Object' .class ∧ ty = void_type ∧ fieldvar = `type' .field], [CSIMPFORWARD : ⊦ i < j ∧ 0 ≤ i → 0 < j], [CSIMPSEQ : ⊦ mkfs (`java.lang.Object' .class, void_type, `type' .field) ' = _type], [CSIMPSEQ : ⊦ (st[rk, val][rk]) = val], [CSIMPSEQ : ⊦ is_obj(r, st) → ¬ is_array(str, r, st)])], [EXTRAFMAS : (r0 -- _type = r -- mkfs(class, ty0, fieldvar) ')]]