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Proof step 73 from proof addarray-disjoint-nosharing-01 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 72:
vals[i→n(i)] = refval(r2), vals[i→n(i0)] = refval(r2), st[r2 -- sks] = refval(r0), st[r2 -- sks1] = refval(r0), r2 -- sks ∈ st, st ⊆ addarray(r, ty, vals, st), is_referencevalue(addarray(r, ty, vals, st)[r -- (i0 ' ' + sks)]), 0 ≤ i0, fits(r2, sks, st), fits(r2, sks1, st), 0 ≤ i, i0 < n→i(# vals), disjoint(str, vals .nonnullrefs, st), validreflist(str, vals, ty, st), newref(r, st), i < n→i(# vals), is_referencevalue(addarray(r, ty, vals, st)[r -- (i ' ' + sks1)]), r2 -- sks1 ∈ st ⊦ i = i0, i0 ' ' + sks = i ' ' + sks1, r = jvmref, vals = [], r0 = jvmref, hasSharing(vals .nonnullrefs, st), junkref(str, r2, st), ∃ r1, m, n. vals[m] = refval(r1) ∧ vals[n] = refval(r1) ∧ r1 ≠ jvmref ∧ m ≠ n ∧ ¬ # vals ≤ m ∧ ¬ # vals ≤ n

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPNAMEDSEQ : nat, , lels, ⊦ ¬ m < n ↔ n ≤ m])]]