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Proof step 203 from proof addarray-put-01 (previous step)

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)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 202:
0 ≤ j, 0 ≤ i0, 0 ≤ i0 + j ⊦ (addarray(r, ty, i0 + j + 1, 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

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPFORWARD : ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j], [CSIMPSEQ : i0 ≠ 0, i0 ≤ i ⊦ ((* i)) ≤ j → ((* i0)) ≤ j], [CSIMPSEQ : ⊦ (~1) < i ↔ 0 ≤ i], [CSIMPSEQ : ⊦ ((* j)) < i0 + ((* j0)) ↔ j - j0 < i0], [CSIMPSEQ : ⊦ ((* j)) ≤ i0 + ((* j0)) ↔ j - j0 ≤ i0], [CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ i ≤ i + j ↔ 0 ≤ j], [CSIMPSEQ : ⊦ i < j + 1 ↔ i ≤ j])]]