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Proof step 83 from proof addarray-disjoint-nosharing-01 (previous step)

st[r1 -- sks1] = refval(r0), st[r2 -- sks] = refval(r0), vals[i→n(i0)] = refval(r2), vals[i→n(i)] = refval(r1), r1 -- sks1 ∈ st, is_referencevalue(addarray(r, ty, vals, st)[r -- (i ' ' + sks1)]), i < n→i(# vals), newref(r, st), disjoint(str, vals .nonnullrefs, st), i0 < n→i(# vals), 0 ≤ i, fits(r1, sks1, st), fits(r2, sks, st), 0 ≤ i0, is_referencevalue(addarray(r, ty, vals, st)[r -- (i0 ' ' + sks)]), st ⊆ addarray(r, ty, vals, st), r2 -- sks ∈ st, r3 ∈ vals .nonnullrefs ⊦ r0 = jvmref, vals = [], r = jvmref, i0 ' ' + sks = i ' ' + sks1, i = i0, r1 = r2, validreflist(str, mkjavavalues(vals .nonnullrefs), mkclasstype(`java.lang.Object' .class), st), junkref(str, r2, st), hasSharing(vals .nonnullrefs, st), dups(vals .nonnullrefs), junkref(str, r1, st), validref(str, r3, ty, st), refval(r3) ∈ vals

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 80:
⊦ r ∈ vals .nonnullrefs ↔ r ≠ jvmref ∧ (∃ m. vals[m] = refval(r) ∧ m < # vals)
Proof step 82:
st[r1 -- sks1] = refval(r0), st[r2 -- sks] = refval(r0), vals[i→n(i0)] = refval(r2), vals[i→n(i)] = refval(r1), r1 -- sks1 ∈ st, is_referencevalue(addarray(r, ty, vals, st)[r -- (i ' ' + sks1)]), i < n→i(# vals), newref(r, st), disjoint(str, vals .nonnullrefs, st), i0 < n→i(# vals), 0 ≤ i, fits(r1, sks1, st), fits(r2, sks, st), 0 ≤ i0, is_referencevalue(addarray(r, ty, vals, st)[r -- (i0 ' ' + sks)]), st ⊆ addarray(r, ty, vals, st), r2 -- sks ∈ st, r3 ≠ jvmref ∧ (∃ m. vals[m] = refval(r3) ∧ m < # vals) ⊦ r0 = jvmref, vals = [], r = jvmref, i0 ' ' + sks = i ' ' + sks1, i = i0, r1 = r2, validreflist(str, mkjavavalues(vals .nonnullrefs), mkclasstype(`java.lang.Object' .class), st), junkref(str, r2, st), hasSharing(vals .nonnullrefs, st), dups(vals .nonnullrefs), junkref(str, r1, st), validref(str, r3, ty, st), refval(r3) ∈ vals

Rule argument

[x0lemmaarg: spec-name: valuesfuns instance-name: lemma-name: nonnullrefs-in antecedent: succedent: r ∈ vals .nonnullrefs ↔ r ≠ jvmref ∧ (∃ m. vals[m] = refval(r) ∧ m < # vals) substlist: [vals, r] → [vals, r3] add preconditions?: F is rewrite lemma?: T current spec?: F rotate lemma?: F replace all?: T paths: ((0, 0, 17)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (vals, r3)]]