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Proof step 192 from proof putarray-addarray-01 (previous step)

0 ≤ n→i(# vals) + i, 0 ≤ j, 0 ≤ i, i ≤ j, j ≤ n→i(# vals) + i, i0 < i + n→i(# vals), 0 ≤ i0, 0 < i + n→i(# vals) ⊦ (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 171:
⊦ j ≤ i ∧ i < n→i(# vals) + j → (putArray(vals, r, j, st)[r -- i ']) = vals[i→n(i - j)]
Proof step 181:
¬ (i ≤ i0 ∧ i0 < n→i(# vals) + i), 0 ≤ n→i(# vals) + i, 0 ≤ j, 0 ≤ i, i ≤ j, j ≤ n→i(# vals) + i, i0 < i + n→i(# vals), 0 ≤ i0, 0 < i + n→i(# vals) ⊦ (putArray(vals, r, i, addarray(r, ty, j, st))[r -- i0 ']) = (mklist(initial_value(ty), i→n(i)) + vals)[i→n(i0)]
Proof step 191:
i ≤ i0 ∧ i0 < n→i(# vals) + i, 0 ≤ n→i(# vals) + i, 0 ≤ j, 0 ≤ i, i ≤ j, j ≤ n→i(# vals) + i, i0 < i + n→i(# vals), 0 ≤ i0, 0 < i + n→i(# vals) ⊦ vals[i→n(i0 - i)] = (mklist(initial_value(ty), i→n(i)) + vals)[i→n(i0)]

Rule argument

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

Additional information

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