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Proof step 167 from proof putarray-addarray-override (previous step)

# vals0 < i→n(i), i0 < i, 0 < i + n→i(# vals) + n→i(# restn(i→n(i) + # vals, vals0)), 0 ≤ i0, i0 < i + n→i(# vals) + n→i(# restn(i→n(i) + # vals, vals0)), i + n→i(# vals) ≤ n→i(# vals0), 0 < i ⊦ (putArray(vals, r0, i, addarray(r0, ty, vals0, st))[r0 -- i0 ']) = (firstn(i→n(i), vals0)[i→n(i0)]), i = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 166:
0 ≤ i ⊦ ((* m)) < i→n(i) ↔ n→i(m) < i

Rule argument

[speclemmaarg: 0 ≤ i ,((* m)) < i→n(i) ↔ n→i(m) < i ,[i, m] → [i, # vals0] ,F ,intnat , ,num-i2n-ls-02 ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ i < j → ¬ j < i], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : ⊦ i ≠ j → (i ≤ j ↔ i < j)], [CSIMPFORWARD : ⊦ i ≤ j ∧ j < j0 → i < j0], [CSIMPSEQ : ⊦ i + j < j ↔ i < 0], [CSIMPSEQ : ⊦ ¬ n→i(n) < 0], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ i + j = j + i])], [EXTRATERMS : (i, # vals0)]]