| ¬ (validrefs(str, r1 ' + refs2, st[r1 -- _type] .type, st) ∧ st[r1 -- _type] .type ≤ ty0), st[r -- mkfs(class, ty0, fieldvar) '] = refval(r1), validrefs(str, r1 ' + refs2, mkclasstype(`java.lang.Object' .class), st), step∃(str, (r1 ' + refs2) .last, r0, st), junkrefs(str, r1 ' + refs1, ty0, st), mkfs(class, ty0, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), is_obj(str, r, st), st[r -- _type] .type ≤ ty, ∀ val, sk, r0, st0, ty, r2, str, refs0. # refs0 < # (r1 + refs1) → (junkrefs(str, r2 ' + refs0, ty, st0) → junkrefs(str, r2 ' + refs0, ty, st0[r0 -- sk, val]) ∨ sk = _type ∨ path∃+(str, r2, r0, st0)) ⊦ r1 = r0, r = r0, r = jvmref, sk = _type, junkrefs(str, r1 ' + refs1, ty0, st[r0 -- sk, val]), validrefs(str, r1 ' + refs2, ty0, st) |
⊦ ¬ validrefs(str, r ' + refs, st[r -- _type] .type, st) → ¬ validrefs(str, r ' + refs, ty, st)
st[r -- mkfs(class, ty0, fieldvar) '] = refval(r1), validrefs(str, r1 ' + refs2, mkclasstype(`java.lang.Object' .class), st), step∃(str, (r1 ' + refs2) .last, r0, st), junkrefs(str, r1 ' + refs1, ty0, st), mkfs(class, ty0, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), is_obj(str, r, st), st[r -- _type] .type ≤ ty, validrefs(str, r1 ' + refs2, st[r1 -- _type] .type, st), ∀ val, sk, r0, st0, ty, r2, str, refs0. # refs0 < # (r1 + refs1) → (junkrefs(str, r2 ' + refs0, ty, st0) → junkrefs(str, r2 ' + refs0, ty, st0[r0 -- sk, val]) ∨ sk = _type ∨ path∃+(str, r2, r0, st0)) ⊦ r1 = r0, r = r0, r = jvmref, sk = _type, junkrefs(str, r1 ' + refs1, ty0, st[r0 -- sk, val]), validrefs(str, r1 ' + refs2, ty0, st), st[r1 -- _type] .type ≤ ty0
[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1])]]