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Proof step 65 from proof addarray-put-01 (previous step)

0 < i0, 0 < i, r -- i ' ∈ addarray(r, ty, val ' + mklist(initial_value(ty), i→n(i0)), st), 0 ≤ i0, i ≤ i0 ⊦ i = 0, r -- i ' ∈ addarray(r, ty, 1 + i0, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 64:
⊦ 0 ≤ j ∧ j < i → r -- j ' ∈ addarray(r, ty, i, st)

Rule argument

[crewrite-arg: in-1dim-16 , F , [st, i, ty, j, r] → [st, 1 + i0, ty, i, r] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : ⊦ i < j → ¬ j < i], [CSIMPSEQ : ⊦ i < j + 1 ↔ i ≤ j], [CSIMPSEQ : ⊦ i ≤ j → (¬ ¬ j < i ↔ false)], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ i + j = j + i])], [EXTRATERMS : (st, 1 + i0, ty, i, r)]]