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Proof step 180 from proof putarray-addarray-01 (previous step)

i0 < j, 0 < i, i0 < i, 0 < i + n→i(# vals), 0 ≤ i0, i0 < i + n→i(# vals), j ≤ n→i(# vals) + i, i ≤ j, 0 ≤ i, 0 ≤ j, 0 ≤ n→i(# vals) + i, i0 < n→i(# vals) + i, 0 < j ⊦ (putArray(vals, r, i, addarray(r, ty, j, st))[r -- i0 ']) = (mklist(initial_value(ty), i→n(i)) + vals)[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 179:
i0 < i ∨ n→i(# vals) + i ≤ i0, i0 < j, 0 < i, i0 < i, 0 < i + n→i(# vals), 0 ≤ i0, i0 < i + n→i(# vals), j ≤ n→i(# vals) + i, i ≤ j, 0 ≤ i, 0 ≤ j, 0 ≤ n→i(# vals) + i, i0 < n→i(# vals) + i, 0 < j ⊦ (addarray(r, ty, j, st)[r -- i0 ']) = (mklist(initial_value(ty), i→n(i)) + vals)[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, r, addarray(r, ty, j, st), i, r, vals] ,F ,storearrays , ,putar-atother ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (i0, r, addarray(r, ty, j, st), i, r, vals)]]