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Proof step 204 from proof addarray-put-01 (previous step)

j < i, 0 ≤ i, 0 ≤ j, 0 < i ⊦ (addarray(r, ty, i, st)[r -- j ', val]) = addarray(r, ty, ((j = 0 ⊃ []; mklist(initial_value(ty), i→n(j)))) + val ' + mklist(initial_value(ty), i→n(i - j + 1)), st)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 203:
i = i0 + j + 1, j < i, 0 ≤ i, 0 ≤ j, 0 < i ⊦ (addarray(r, ty, i, st)[r -- j ', val]) = addarray(r, ty, ((j = 0 ⊃ []; mklist(initial_value(ty), i→n(j)))) + val ' + mklist(initial_value(ty), i→n(i0)), st)

Rule argument

[speclemmaarg: ,i0 = i - j ↔ i = i0 + j ,[i, j, i0] → [i, j + 1, i0] ,T ,int-abs , ,elim-sub ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : ⊦ i0 = i - j ↔ i = i0 + j])], [EXTRATERMS : (i, j + 1, i0)]]