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Proof step 202 from proof hasSharing-addobj-same (previous step)

fis[sk0] = refval(r3), st[r3 -- sks0] = refval(r2), st[r0 -- sks] = refval(r2), fis[sk] = refval(r0), validfieldinits(str, fis, st), newref(r, st), fits(r0, sks, st), fits(r3, sks0, st), sk ∈ fis, sk0 ∈ fis, sk ∈ fis .keys, sk0 ∈ fis .keys, is_referencevalue(addobj(r, class, fis, st)[r -- (sk ' + sks)]) ⊦ sk = sk0, r3 = jvmref, r3 = r0, r2 = jvmref, r = jvmref, r0 = jvmref, junkref(str, r3, st), junkref(str, r0, st), junkref(str, r, addobj(r, class, fis, st)), dups(fis .vals .nonnullrefs), hasSharing(fis .vals .nonnullrefs, st), (addobj(r, class, fis, st)[r0 -- sks]) .refval ≠ jvmref ∧ (addobj(r, class, fis, st)[r0 -- sks]) = (addobj(r, class, fis, st)[r -- (sk0 ' + sks0)])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 191:
⊦ st ⊆ st0 ∧ r -- sks ∈ st → st0[r -- sks] = st[r -- sks]
Proof step 192:
⊦ ¬ junkref(str, r, st) ∧ fits(r, sks, st) ∧ r ≠ jvmref → r -- sks ∈ st
Proof step 201:
st ⊆ addobj(r, class, fis, st) ∧ r0 -- sks ∈ st, fis[sk0] = refval(r3), st[r3 -- sks0] = refval(r2), st[r0 -- sks] = refval(r2), fis[sk] = refval(r0), validfieldinits(str, fis, st), newref(r, st), fits(r0, sks, st), fits(r3, sks0, st), sk ∈ fis, sk0 ∈ fis, sk ∈ fis .keys, sk0 ∈ fis .keys, is_referencevalue(addobj(r, class, fis, st)[r -- (sk ' + sks)]) ⊦ sk = sk0, r3 = jvmref, r3 = r0, r2 = jvmref, r = jvmref, r0 = jvmref, junkref(str, r3, st), junkref(str, r0, st), junkref(str, r, addobj(r, class, fis, st)), dups(fis .vals .nonnullrefs), hasSharing(fis .vals .nonnullrefs, st), st[r0 -- sks] .refval ≠ jvmref ∧ st[r0 -- sks] = (addobj(r, class, fis, st)[r -- (sk0 ' + sks0)])

Rule argument

[x0lemmaarg: spec-name: storefuns instance-name: lemma-name: lookup-subset-01 antecedent: succedent: st ⊆ st0 ∧ r -- sks ∈ st → st0[r -- sks] = st[r -- sks] substlist: [st, st0, r, sks] → [st, addobj(r, class, fis, st), r0, sks] add preconditions?: F is rewrite lemma?: T current spec?: F rotate lemma?: F replace all?: T paths: ((1, 0, 11, 1, 0, 1, 0, 1, 0)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPNAMEDSEQ : addfuns, , stsubset-addobj, ⊦ newref(r, st) → ( st ⊆ addobj (r, class1, fis, st0) ↔ st ⊆ st0)], [CSIMPNAMEDSEQ : store, javastore, sub-ref, ⊦ st ⊆ st])], [EXTRATERMS : (st, addobj(r, class, fis, st), r0, sks)]]