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

validreflist(str, mkjavavalues(refs), mkclasstype(`java.lang.Object' .class), st), st[refs[i→n(i0)] -- sks] = refval(r0), st[refs[i→n(i)] -- sks1] = refval(r0), refs[i→n(i0)] -- sks ∈ st, st ⊆ addarray(r, ty, mkjavavalues(refs), st), is_referencevalue(addarray(r, ty, mkjavavalues(refs), st)[r -- (i ' ' + sks1)]), is_referencevalue(addarray(r, ty, mkjavavalues(refs), st)[r -- (i0 ' ' + sks)]), i→n(i) < # refs, 0 ≤ i0, fits(refs[i→n(i0)], sks, st), fits(refs[i→n(i)], sks1, st), ∀ r1, sks1, r2, sks2. ¬ (r1 ∈ refs ∧ r2 ∈ refs ∧ r1 ≠ r2 ∧ fits(r1, sks1, st) ∧ fits(r2, sks2, st) ∧ st[r1 -- sks1] = st[r2 -- sks2] ∧ st[r1 -- sks1] .refval ≠ jvmref), validreflist(str, mkjavavalues(refs), ty, st), newref(r, st), 0 ≤ i, i→n(i0) < # refs, i0 < n→i(# refs), i < n→i(# refs), refs[i→n(i)] -- sks1 ∈ st ⊦ i0 ' ' + sks = i ' ' + sks1, r = jvmref, refs = [], r0 = jvmref, i0 = i, junkref(str, refs[i→n(i)], st), dups(refs), hasSharing(refs, st), junkref(str, refs[i→n(i0)], st)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 66:
st[refs[i→n(i0)] -- sks] = refval(r0), st[refs[i→n(i)] -- sks1] = refval(r0), validreflist(str, mkjavavalues(refs), mkclasstype(`java.lang.Object' .class), st), refs[i→n(i0)] -- sks ∈ st, st ⊆ addarray(r, ty, mkjavavalues(refs), st), is_referencevalue(addarray(r, ty, mkjavavalues(refs), st)[r -- (i ' ' + sks1)]), is_referencevalue(addarray(r, ty, mkjavavalues(refs), st)[r -- (i0 ' ' + sks)]), i→n(i) < # refs, 0 ≤ i0, fits(refs[i→n(i0)], sks, st), fits(refs[i→n(i)], sks1, st), validreflist(str, mkjavavalues(refs), ty, st), newref(r, st), 0 ≤ i, i→n(i0) < # refs, i0 < n→i(# refs), i < n→i(# refs), refs[i→n(i)] -- sks1 ∈ st, ∀ r1, sks0, r2, sks2. ¬ r1 ∈ refs ∨ ¬ r2 ∈ refs ∨ r1 = r2 ∨ ¬ fits(r1, sks0, st) ∨ ¬ fits(r2, sks2, st) ∨ st[r1 -- sks0] ≠ st[r2 -- sks2] ∨ st[r1 -- sks0] .refval = jvmref ⊦ i0 ' ' + sks = i ' ' + sks1, r = jvmref, refs = [], r0 = jvmref, i0 = i, junkref(str, refs[i→n(i)], st), dups(refs), hasSharing(refs, st), junkref(str, refs[i→n(i0)], st)

Rule argument

[emptyarg]

Additional information

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