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Proof step 205 from proof addarray-put-01 (conclusion)

⊦ 0 ≤ i ∧ 0 ≤ j ∧ j < 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 simplifier applied rule simplifier

And obtained the following new goals

Proof step 204:
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)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPFORWARD : ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j], [CSIMPFORWARD : ⊦ i < j ∧ 0 ≤ i → 0 < j], [CSIMPSEQ : ⊦ val + vals = val ' + vals])]]