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Proof step 163 from proof hasSharing-addobj-same (previous step)

st[r0 -- sks0] = refval(r1), fis .keys = instfields(class), st[r0 -- sks] = refval(r1), r0 ∈ fis .vals .nonnullrefs, fits(r0, sks, st), fits(r0, sks0, st), newref(r, st), validfieldinits(str, fis, st) ⊦ sks0 = sks, sks0 = [], sks = [], r1 = jvmref, r = jvmref, dups(fis .vals .nonnullrefs), ∃ sks1, sks2. fits(r, sks1, addobj(r, class, fis, st)) ∧ fits(r, sks2, addobj(r, class, fis, st)) ∧ sks1 ≠ sks2 ∧ (addobj(r, class, fis, st)[r -- sks1]) .refval ≠ jvmref ∧ (addobj(r, class, fis, st)[r -- sks1]) = (addobj(r, class, fis, st)[r -- sks2]), junkref(str, r, addobj(r, class, fis, st))

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

[x0lemmaarg: spec-name: okfuns instance-name: lemma-name: nonnullrefs-in-key antecedent: succedent: ¬ dups(fis .keys) → ( r ∈ fis .vals .nonnullrefs ↔ r ≠ jvmref ∧ (∃ sk. fis[sk] = refval(r) ∧ sk ∈ fis)) substlist: [fis, r] → [fis, r0] add preconditions?: F is rewrite lemma?: T current spec?: F rotate lemma?: F replace all?: T paths: ((0, 0, 3)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPNAMEDSEQ : addfuns, , instfields-nodups, ⊦ ¬ dups(instfields(class))])], [EXTRATERMS : (fis, r0)]]