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Proof step 177 from proof putarray-addarray-override (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 172:
⊦ i < j ∨ n→i(# vals) + j ≤ i → (putArray(vals, r, j, st)[r0 -- i ']) = st[r0 -- i ']
Proof step 176:
i0 < i ∨ n→i(# vals) + i ≤ i0, 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, i0 < i ⊦ (addarray(r0, ty, vals0, st)[r0 -- i0 ']) = vals0[i→n(i0)]

Rule argument

[speclemmaarg: , i < j ∨ n→i(# vals) + j ≤ i → (putArray(vals, r, j, st)[r0 -- i ']) = st[r0 -- i '] ,[i, r0, st, j, r, vals] → [i0, r0, addarray(r0, ty, vals0, st), i, r0, vals] ,F ,storearrays , ,putar-atother ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (i0, r0, addarray(r0, ty, vals0, st), i, r0, vals)]]