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Proof step 88 from proof putarray-addarray-01 (previous step)

0 ≤ i, 0 ≤ i0 + n→i(# vals), 0 ≤ i0 + i + n→i(# vals), 0 < i0 ⊦ (r -- i1 ' ∈ addarray(r, ty, i0 + i + n→i(# vals), st) ∨ i ≤ i1 ∧ i1 < i + n→i(# vals) ↔ r -- i1 ' ∈ st ∨ ¬ i1 < 0 ∧ ¬ i + n→i(# vals) + i0 ≤ i1) ∧ (putArray(vals, r, i, addarray(r, ty, i0 + i + n→i(# vals), st))[r -- i1 ']) = (addarray(r, ty, mklist(initial_value(ty), i→n(i)) + vals + mklist(initial_value(ty), i→n(i0)), st)[r -- i1 '])

User applied rule case distinction

And obtained the following new goals

Proof step 14:
0 ≤ i, 0 ≤ i0 + n→i(# vals), 0 ≤ i0 + i + n→i(# vals), 0 < i0 ⊦ r -- i1 ' ∈ addarray(r, ty, i0 + i + n→i(# vals), st) ∨ i ≤ i1 ∧ i1 < i + n→i(# vals) ↔ r -- i1 ' ∈ st ∨ ¬ i1 < 0 ∧ ¬ i + n→i(# vals) + i0 ≤ i1
Proof step 87:
0 ≤ i, 0 ≤ i0 + n→i(# vals), 0 ≤ i0 + i + n→i(# vals), 0 < i0 ⊦ (putArray(vals, r, i, addarray(r, ty, i0 + i + n→i(# vals), st))[r -- i1 ']) = (addarray(r, ty, mklist(initial_value(ty), i→n(i)) + vals + mklist(initial_value(ty), i→n(i0)), st)[r -- i1 '])

Rule argument

[CASEDARG : pos: right 1, ()]

Additional information

[[CONCRETESIMPRULES : ()]]