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Proof step 181 from proof putarray-addarray-override (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 170:
⊦ n→i(n) < j → (getarray(r, i, j, st)[n]) = st[r -- (i + n→i(n)) ']
Proof step 180:
n→i(i→n(i0)) < i, i0 < i, 0 < 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, i→n(i) ≤ # vals0 ⊦ (putArray(vals, r0, i, addarray(r0, ty, vals0, st))[r0 -- (0 + n→i(i→n(i0))) ']) = vals0[i→n(i0)]

Rule argument

[speclemmaarg: ,n→i(n) < j → (getarray(r, i, j, st)[n]) = st[r -- (i + n→i(n)) '] ,[n, st, j, i, r] → [i→n(i0), putArray(vals, r0, i, addarray(r0, ty, vals0, st)), i, 0, r0] ,F ,storearrays , ,get-get ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ 0 ≤ i → n→i(i→n(i)) = i], [CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ i < j → (¬ ¬ j ≤ i ↔ false)])], [EXTRATERMS : (i→n(i0), putArray(vals, r0, i, addarray(r0, ty, vals0, st)), i, 0, r0)]]