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Proof step 12 from proof addarray-disjoint-nosharing (previous step)

(mkjavavalues(refs)[i→n(i0)]) = refval(r2), (addarray(r, ty, mkjavavalues(refs), st)[r -- (i0 ' ' + sks)]) = refval(r0), (addarray(r, ty, mkjavavalues(refs), st)[r -- (i ' ' + sks1)]) = refval(r0), # refs ≤ i→n(i0), i→n(i) < # refs, 0 ≤ i0, fits(r2, sks, addarray(r, ty, mkjavavalues(refs), st)), fits(refs[i→n(i)], sks1, addarray(r, ty, mkjavavalues(refs), st)), disjoint(str, refs, st), validreflist(str, mkjavavalues(refs), ty, st), newref(r, st), 0 ≤ i, i0 < n→i(# refs), i < i0, i < n→i(# refs), 0 < i0 ⊦ i0 ' ' + sks = i ' ' + sks1, r = jvmref, refs = [], r0 = jvmref, # refs = 1, dups(refs), hasSharing(refs, st)

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, # refs] add preconditions?: F is rewrite lemma?: T current spec?: F rotate lemma?: F replace all?: T paths: ((0, 0, 3)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ i < j → (¬ ¬ j ≤ i ↔ false)])], [EXTRATERMS : (i0, # refs)]]