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Proof step 166 from proof addarray-put-01 (previous step)

i→n(i) = (m + 1) + i→n(j), 1 < i0 + j, 1 < i, 0 < i, i ≤ j + i0, 0 ≤ i, i ≤ i0 + j, 0 < j, 0 ≤ i0 + j, 0 ≤ i0, 0 < i0, j < i, i→n(i0) ≤ m ⊦ j = 0, i = j, initial_value(ty) = (mklist(initial_value(ty), i→n(i0))[m])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 162:
i < 0 ⊦ i→n(i) = ((* m)) ↔ ~ i = n→i(m)
Proof step 165:
¬ i < 0, i→n(i) = (m + 1) + i→n(j), 1 < i0 + j, 1 < i, 0 < i, i ≤ j + i0, 0 ≤ i, i ≤ i0 + j, 0 < j, 0 ≤ i0 + j, 0 ≤ i0, 0 < i0, j < i, i→n(i0) ≤ m ⊦ j = 0, i = j, initial_value(ty) = (mklist(initial_value(ty), i→n(i0))[m])

Rule argument

[speclemmaarg: i < 0 ,i→n(i) = ((* m)) ↔ ~ i = n→i(m) ,[m, i] → [(m + 1) + i→n(j), i] ,F ,intnat , ,num-i2n-eq-01 ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ n→i(m + n) = n→i(m) + n→i(n)], [CSIMPSEQ : ⊦ 0 < i → n→i(i→n(i)) = i], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ m + n = n + m], [CSIMPSEQ : ⊦ ~ i = j ↔ i + j = 0], [CSIMPSEQ : ⊦ ((* j)) = i0 + ((* j0)) ↔ j - j0 = i0], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ i < j → ¬ j < i])], [EXTRATERMS : ((m + 1) + i→n(j), i)]]