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Proof step 58 from proof addarray-disjoint-nosharing (previous step)

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), disjoint(str, refs, st), newref(r, st), 0 ≤ i, i→n(i0) < # refs, i0 < n→i(# refs), i < n→i(# refs), refs[i→n(i)] -- sks1 ∈ st, ∀ val. val ∈ mkjavavalues(refs) → val = refval(jvmref), refval(refs[i→n(i0)]) ∈ mkjavavalues(refs) → refs[i→n(i0)] = jvmref ⊦ i0 ' ' + sks = i ' ' + sks1, r = jvmref, refs = [], r0 = jvmref, i0 = i, is_classtype(ty), is_arraytype(ty), junkref(str, refs[i→n(i)], st), dups(refs), hasSharing(refs, st), junkref(str, refs[i→n(i0)], st), validreflist(str, mkjavavalues(refs), mkclasstype(`java.lang.Object' .class), st)

User applied rule case distinction

And obtained the following new goals

Proof step 56:
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), disjoint(str, refs, st), newref(r, st), 0 ≤ i, i→n(i0) < # refs, i0 < n→i(# refs), i < n→i(# refs), refs[i→n(i)] -- sks1 ∈ st, ∀ val. val ∈ mkjavavalues(refs) → val = refval(jvmref) ⊦ refval(refs[i→n(i0)]) ∈ mkjavavalues(refs), i0 ' ' + sks = i ' ' + sks1, r = jvmref, refs = [], r0 = jvmref, i0 = i, is_classtype(ty), is_arraytype(ty), junkref(str, refs[i→n(i)], st), dups(refs), hasSharing(refs, st), junkref(str, refs[i→n(i0)], st), validreflist(str, mkjavavalues(refs), mkclasstype(`java.lang.Object' .class), st)
Proof step 57:
⊦ fits(jvmref, sks, st) ↔ sks = []

Rule argument

[CASEDARG : pos: left 19, ()]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ junkref(str, jvmref, st)], [CSIMPSEQ : ⊦ st[r -- []] = refval(r)], [CSIMPSEQ : ⊦ refval(r) = refval(r0) ↔ r = r0])]]