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Proof step 9 from proof addarray-disjoint-nosharing (previous step)

¬ i→n(i) < # refs, (addarray(r, ty, mkjavavalues(refs), st)[r -- (i0 ' ' + sks)]) = refval(r0), (addarray(r, ty, mkjavavalues(refs), st)[r -- (i ' ' + sks1)]) = refval(r0), (mkjavavalues(refs)[i→n(i)]) = refval(r1), (mkjavavalues(refs)[i→n(i0)]) = refval(r2), 0 ≤ i0, fits(r2, sks, addarray(r, ty, mkjavavalues(refs), st)), fits(r1, sks1, addarray(r, ty, mkjavavalues(refs), st)), disjoint(str, refs, st), validreflist(str, mkjavavalues(refs), ty, st), newref(r, st), 0 ≤ i, i < n→i(# refs), i0 < n→i(# refs) ⊦ i0 ' ' + sks = i ' ' + sks1, r = jvmref, refs = [], r0 = jvmref, dups(refs), hasSharing(refs, st)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
(addarray(r, ty, mkjavavalues(refs), st)[r -- (i0 ' ' + sks)]) = refval(r0), (addarray(r, ty, mkjavavalues(refs), st)[r -- (i ' ' + sks1)]) = refval(r0), (mkjavavalues(refs)[i→n(i)]) = refval(r1), (mkjavavalues(refs)[i→n(i0)]) = refval(r2), 0 ≤ i0, fits(r2, sks, addarray(r, ty, mkjavavalues(refs), st)), fits(r1, sks1, addarray(r, ty, mkjavavalues(refs), st)), disjoint(str, refs, st), validreflist(str, mkjavavalues(refs), ty, st), newref(r, st), 0 ≤ i, i < n→i(# refs), i0 < n→i(# refs), # refs ≤ i→n(i) ⊦ i0 ' ' + sks = i ' ' + sks1, r = jvmref, refs = [], r0 = jvmref, dups(refs), hasSharing(refs, st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ m < n ↔ n ≤ m])]]