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Proof step 194 from proof putarray-addarray-01 (previous step)

0 ≤ n→i(# vals) + i, 0 ≤ j, 0 ≤ i, i ≤ j, j ≤ n→i(# vals) + i ⊦ (putArray(vals, r, i, addarray(r, ty, j, st))[r -- i0 ']) = (addarray(r, ty, mklist(initial_value(ty), i→n(i)) + vals, st)[r -- i0 '])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 156:
⊦ 0 ≤ i ∧ i < n→i(# vals) → (addarray(r, ty, vals, st)[r -- i ']) = vals[i→n(i)]
Proof step 170:
¬ (0 ≤ i0 ∧ i0 < n→i(# (mklist(initial_value(ty), i→n(i)) + vals))), 0 ≤ n→i(# vals) + i, 0 ≤ j, 0 ≤ i, i ≤ j, j ≤ n→i(# vals) + i ⊦ (putArray(vals, r, i, addarray(r, ty, j, st))[r -- i0 ']) = (addarray(r, ty, mklist(initial_value(ty), i→n(i)) + vals, st)[r -- i0 '])
Proof step 193:
0 ≤ i0 ∧ i0 < n→i(# (mklist(initial_value(ty), i→n(i)) + vals)), 0 ≤ n→i(# vals) + i, 0 ≤ j, 0 ≤ i, i ≤ j, j ≤ n→i(# vals) + i ⊦ (putArray(vals, r, i, addarray(r, ty, j, st))[r -- i0 ']) = (mklist(initial_value(ty), i→n(i)) + vals)[i→n(i0)]

Rule argument

[crewrite-arg: add-at-ok , F , [i, st, vals, ty, r] → [i0, st, mklist(initial_value(ty), i→n(i)) + vals, ty, r] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (i0, st, mklist(initial_value(ty), i→n(i)) + vals, ty, r)]]