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Proof step 10 from proof addarray-disjoint-nosharing-01 (previous step)

vals[i→n(i)] = refval(r1), (addarray(r, ty, vals, st)[r2 -- sks]) = refval(r0), (addarray(r, ty, vals, st)[r1 -- sks1]) = refval(r0), is_referencevalue(addarray(r, ty, vals, st)[r -- (i0 ' ' + sks)]), 0 ≤ i0, fits(r2, sks, addarray(r, ty, vals, st)), fits(r1, sks1, addarray(r, ty, vals, st)), 0 ≤ i, i0 < n→i(# vals), disjoint(str, vals .nonnullrefs, st), newref(r, st), i < n→i(# vals), is_referencevalue(addarray(r, ty, vals, st)[r -- (i ' ' + sks1)]), junkref(str, r2, st), # vals ≤ i→n(i0) ⊦ i0 ' ' + sks = i ' ' + sks1, r = jvmref, vals = [], r0 = jvmref, dups(vals .nonnullrefs), hasSharing(vals .nonnullrefs, st), vals[i→n(i0)] ∈ vals

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
0 ≤ i ⊦ ((* m)) ≤ i→n(i) ↔ n→i(m) ≤ i

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: ((0, 0, 14)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPNAMEDSEQ : int-abs, , lels-04, ⊦ i ≤ j → (¬ ¬ j < i ↔ false)])], [EXTRATERMS : (i0, # vals)]]