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Proof step 155 from proof putarray-addarray-override (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 121:
i < 0 ⊦ i→n(i) = ((* m)) ↔ ~ i = n→i(m)
Proof step 154:
¬ i0 < 0, i→n(i0) = n + i→n(i), i ≤ i0, i→n(i) + # vals ≤ # vals0, 0 ≤ i0, i0 < n→i(# vals0), 0 ≤ i, i→n(i) < # vals0 ⊦ (putArray(vals, r0, i, addarray(r0, ty, vals0, st))[r0 -- i0 ']) = (vals + restn(i→n(i) + # vals, vals0))[n], vals0 = []

Rule argument

[speclemmaarg: i < 0 ,i→n(i) = ((* m)) ↔ ~ i = n→i(m) ,[m, i] → [n + i→n(i), i0] ,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 : ⊦ i ≤ j → (¬ ¬ j < i ↔ false)])], [EXTRATERMS : (n + i→n(i), i0)]]