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Proof step 46 from proof junkrefs-put-nopathexplus-equiv (previous step)

st[r -- mkfs(class, ty0, fieldvar) '] = refval(r1), 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, 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, r = jvmref, sk = _type, junkrefs(str, r1 ' + refs1, ty0, st[r0 -- sk, val]), ∃ refs. refs ≠ [] ∧ refs .first = r ∧ validrefs(str, refs, mkclasstype(`java.lang.Object' .class), st) ∧ step∃(str, refs .last, r0, st)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 45:
st[r -- mkfs(class, ty0, fieldvar) '] = refval(refs .first), step∃(str, refs .last, r0, st), validrefs(str, refs, mkclasstype(`java.lang.Object' .class), st), st[r -- _type] .type ≤ ty, is_obj(str, r, st), mkfs(class, ty0, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), junkrefs(str, refs .first ' + refs1, ty0, st), ∀ val, sk, r0, st0, ty, r2, str, refs0. # refs0 < # (refs .first + refs1) → (junkrefs(str, r2 ' + refs0, ty, st0) → junkrefs(str, r2 ' + refs0, ty, st0[r0 -- sk, val]) ∨ sk = _type ∨ path∃+(str, r2, r0, st0)) ⊦ refs = [], sk = _type, r = jvmref, r = r0, refs .first = r0, junkrefs(str, refs .first ' + refs1, ty0, 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

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1])]]