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Proof step 170 from proof hasSharing-put-index-refval (previous step)

(st[r -- i ', refval(r2)][r2 -- ((sks3 + i ' ' + sks4) + i ' ' + sks0)]) = refval(r1), st[r -- _type] .type = mkarraytype(ty), st[r2 -- sks1] = refval(r1), st[r2 -- (sks3 + i ' ' + sks4)] = refval(r), (st[r -- i ', refval(r2)][r2 -- (sks3 + i ' ' + sks4)]) = refval(r0), st[r2 -- sks3] = refval(r), 0 < st[r -- _length] .intval, is_referencevalue(st[r -- i ', refval(r2)][r -- (i ' ' + sks1)]), fits(r2, sks1, st), i < st[r -- _length] .intval, 0 ≤ i, fits(r2, sks3 + i ' ' + sks4, st[r -- i ', refval(r2)]), fits(r0, i ' ' + sks0, st[r -- i ', refval(r2)]), disjoint(str, r ' + r2 ', st), validref(str, r2, ty, st) ⊦ r = jvmref, r = r2, r1 = jvmref, r2 = jvmref, sks1 = (sks3 + i ' ' + sks4) + i ' ' + sks0, junkref(str, r, st), hasSharing(r2, st), hasSharing(r, st), ∃ sks2, sks0. sks1 = sks2 + i ' ' + sks0 ∧ st[r2 -- sks2] .refval = r ∧ (∀ sks3. sks3 + i ' ' ⊑ sks2 → st[r2 -- sks3] .refval ≠ st[r2 -- sks2] .refval), ∃ sks2. ¬ (sks2 + i ' ' ⊑ sks3 + i ' ' + sks4 → st[r2 -- sks2] .refval ≠ r), ∃ sks2. ¬ (sks2 + i ' ' ⊑ sks3 → st[r2 -- sks2] .refval ≠ r)

User applied rule exists right

And closed the goal!

Rule argument

[EXRARG : pos: right 10, [extquanttermlist: (sks3)abort:F, discard:T, computed:F]]

Additional information

[[CONCRETESIMPRULES : ([CSIMPNAMEDSEQ : list-last, storekeys, app-01-02, ⊦ sks + sks0 ⊑ sks + sks1 ↔ sks0 ⊑ sks1], [CSIMPNAMEDSEQ : list-last, storekeys, prefix-one, ⊦ sk ' ⊑ sk0 ' + sks ↔ sk = sk0], [CSIMPNAMEDSEQ : list, storekeys, a, ⊦ (sks + sks0) + sks1 = sks + sks0 + sks1], [CSIMPNAMEDSEQ : javavalue, , sel-09, ⊦ refval(r) .refval = r])], [EXTRATERMS : (sks3)]]