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Proof step 53 from proof hasSharing-addobj-same (previous step)

fis[sk0] = refval(r2), fis[sk] = refval(r1), st[r1 -- sks1] = refval(r0), fis .keys = instfields(class), st[r2 -- sks] = refval(r0), fits(r1, sks1, st), sk ∈ instfields(class), is_referencevalue(addobj(r, class, fis, st)[r -- (sk ' + sks1)]), is_referencevalue(addobj(r, class, fis, st)[r -- (sk0 ' + sks)]), sk ∈ fis, validfieldinits(str, fis, st), newref(r, st), fits(r2, sks, st), sk0 ∈ instfields(class), sk0 ∈ fis, r1 -- sks1 ∈ st, r2 -- sks ∈ st, validreflist(str, mkjavavalues(fis .vals .nonnullrefs), mkclasstype(`java.lang.Object' .class), st), ¬ r1 ∈ fis .vals .nonnullrefs ∨ ¬ r2 ∈ fis .vals .nonnullrefs ⊦ r0 = jvmref, sk0 ' + sks = sk ' + sks1, r = jvmref, sk = sk0, r1 = r2, junkref(str, r2, st), junkref(str, r1, st), junkref(str, r, addobj(r, class, fis, st)), hasSharing(fis .vals .nonnullrefs, st), dups(fis .vals .nonnullrefs)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 45:
⊦ fis[sk] = refval(r) ∧ sk ∈ fis ∧ r ≠ jvmref → r ∈ fis .vals .nonnullrefs
Proof step 46:
⊦ ¬ junkref(str, r, st) ∧ fits(r, sks, st) ∧ r ≠ jvmref → r -- sks ∈ st
Proof step 47:
⊦ fits(jvmref, sks, st) ↔ sks = []
Proof step 52:
fis[sk] = refval(r1) ∧ sk ∈ fis ∧ r1 ≠ jvmref, fis[sk0] = refval(r2), fis[sk] = refval(r1), st[r1 -- sks1] = refval(r0), fis .keys = instfields(class), st[r2 -- sks] = refval(r0), fits(r1, sks1, st), sk ∈ instfields(class), is_referencevalue(addobj(r, class, fis, st)[r -- (sk ' + sks1)]), is_referencevalue(addobj(r, class, fis, st)[r -- (sk0 ' + sks)]), sk ∈ fis, validfieldinits(str, fis, st), newref(r, st), fits(r2, sks, st), sk0 ∈ instfields(class), sk0 ∈ fis, r1 -- sks1 ∈ st, r2 -- sks ∈ st, validreflist(str, mkjavavalues(fis .vals .nonnullrefs), mkclasstype(`java.lang.Object' .class), st), ¬ true ∨ ¬ r2 ∈ fis .vals .nonnullrefs ⊦ r0 = jvmref, sk0 ' + sks = sk ' + sks1, r = jvmref, sk = sk0, r1 = r2, junkref(str, r2, st), junkref(str, r1, st), junkref(str, r, addobj(r, class, fis, st)), hasSharing(fis .vals .nonnullrefs, st), dups(fis .vals .nonnullrefs)

Rule argument

[x0lemmaarg: spec-name: okfuns instance-name: lemma-name: nonnullrefs-in antecedent: succedent: fis[sk] = refval(r) ∧ sk ∈ fis ∧ r ≠ jvmref → r ∈ fis .vals .nonnullrefs substlist: [fis, sk, r] → [fis, sk, r1] add preconditions?: F is rewrite lemma?: T current spec?: F rotate lemma?: F replace all?: T paths: ((0, 0, 18, 1, 0, 1, 0)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPNAMEDSEQ : junkrefs, , junkref-null, ⊦ ¬ junkref(str, jvmref, st)], [CSIMPNAMEDSEQ : okfuns, , nonnullrefs-in, ⊦ fis[sk] = refval(r) ∧ sk ∈ fis ∧ r ≠ jvmref → r ∈ fis .vals .nonnullrefs], [CSIMPNAMEDSEQ : storefuns, , lookup-empty, ⊦ st[r -- []] = refval(r)], [CSIMPNAMEDSEQ : javavalue, , inj-03, ⊦ refval(r) = refval(r0) ↔ r = r0])], [EXTRATERMS : (fis, sk, r1)]]