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Proof step 41 from proof validrefs-set-null (previous step)

acc + refs0 = r0 ' + refs1, st[r -- i '] = refval(r0), is_array(str, r, st), 0 < st[r -- _length] .intval, 0 ≤ i, validrefs(str, acc + refs0, st[r -- _type] .type .type, st), i < st[r -- _length] .intval, st[r -- _type] .type ≤ ty, is_reftype(ty1), is_obj(str, acc .last, st), mkfs(class, ty1, fieldvar) ' ∈ instfields(st[acc .last -- _type] .type .class), ∀ str0, refs, ty0, st0, fs. validrefs(str0, acc + refs, ty0, st0) ∧ is_obj(str0, acc .last, st0) ∧ fs ' ∈ instfields(st0[acc .last -- _type] .type .class) ∧ is_reftype(fs .type) ∧ refs ≠ [] → validrefs(str0, acc + jvmref ', ty0, st0[acc .last -- fs ', refval(jvmref)]) ⊦ acc = [], refs0 = [], r = jvmref, acc + refs0 = [], dups(acc), r ∈ acc, validrefs(str, (r ' + acc) + jvmref ', ty, st[acc .last -- mkfs(class, ty1, fieldvar) ', refval(jvmref)]), ¬ r0 ∈ acc ∧ ¬ r0 ∈ refs0, is_array(str, r, st[acc .last -- mkfs(class, ty1, fieldvar) ', refval(jvmref)]) ∧ (st[acc .last -- mkfs(class, ty1, fieldvar) ', refval(jvmref)][r -- _type]) .type ≤ ty

Heuristic weak cut applied rule cut formula

And closed the goal!

Rule argument

[fma-arg: r -- _type = acc .last -- mkfs(class, ty1, fieldvar) ']

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ refs .last = r ∧ refs ≠ [] → r ∈ refs], [CSIMPSEQ : ⊦ r -- sk = r0 -- sk0 ↔ r = r0 ∧ sk = sk0], [CSIMPSEQ : ⊦ r -- sk = r0 -- sk0 ↔ ¬ ¬ (r = r0 ∧ sk = sk0)], [CSIMPSEQ : ⊦ is_array(str, r, st) → ¬ is_obj(str, r, st)], [CSIMPSEQ : ⊦ r ≠ r0 → ( is_array (str, r0, st[r -- sk, val]) ↔ is_array(str, r0, st))], [CSIMPSEQ : ⊦ r ≠ r0 → (st[r0 -- sk0, val][r -- sk]) = st[r -- sk]])], [EXTRAFMAS : (r -- _type = acc .last -- mkfs(class, ty1, fieldvar) ')]]