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Proof step 67 from proof addarray-disjoint-nosharing-01 (previous step)

vals[i→n(i)] = refval(r2), vals[i→n(i0)] = refval(r2), st[r2 -- sks] = refval(r0), st[r2 -- sks1] = refval(r0), st ⊆ addarray(r, ty, vals, st), is_referencevalue(addarray(r, ty, vals, st)[r -- (i0 ' ' + sks)]), 0 ≤ i0, fits(r2, sks, st), fits(r2, sks1, st), 0 ≤ i, i0 < n→i(# vals), disjoint(str, vals .nonnullrefs, st), validreflist(str, vals, ty, st), newref(r, st), i < n→i(# vals), is_referencevalue(addarray(r, ty, vals, st)[r -- (i ' ' + sks1)]) ⊦ i = i0, i0 ' ' + sks = i ' ' + sks1, r = jvmref, vals = [], r0 = jvmref, r2 = jvmref, hasSharing(vals .nonnullrefs, st), junkref(str, r2, st), ¬ # vals ≤ i→n(i0) ∧ ¬ # vals ≤ i→n(i)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

[x0lemmaarg: spec-name: intnat instance-name: lemma-name: num-i2n-le-02 antecedent: 0 ≤ i succedent: ((* m)) ≤ i→n(i) ↔ n→i(m) ≤ i substlist: [i, m] → [i0, # vals] add preconditions?: F is rewrite lemma?: T current spec?: F rotate lemma?: F replace all?: T paths: ((1, 0, 8, 1, 0, 1, 0)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (i0, # vals)]]