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Proof step 85 from proof addarray-put-01 (previous step)

0 ≤ i0 + j, 0 ≤ i0, 0 ≤ j, r -- i ' ∈ addarray(r, ty, ((j = 0 ⊃ []; mklist(initial_value(ty), i→n(j)))) + val ' + mklist(initial_value(ty), i→n(i0)), st), i ≤ n→i(# ((j = 0 ⊃ []; mklist(initial_value(ty), i→n(j))))) + i0, 0 ≤ n→i(# ((j = 0 ⊃ []; mklist(initial_value(ty), i→n(j))))) + i0, 0 ≤ i ⊦ i = j, r -- i ' ∈ addarray(r, ty, i0 + j + 1, st)

User applied rule case distinction

And obtained the following new goals

Proof step 71:
j = 0, i ≤ n→i(# []) + i0, 0 ≤ i0 + j, 0 ≤ i0, 0 ≤ j, r -- i ' ∈ addarray(r, ty, ((j = 0 ⊃ []; mklist(initial_value(ty), i→n(j)))) + val ' + mklist(initial_value(ty), i→n(i0)), st), 0 ≤ n→i(# ((j = 0 ⊃ []; mklist(initial_value(ty), i→n(j))))) + i0, 0 ≤ i ⊦ i = j, r -- i ' ∈ addarray(r, ty, i0 + j + 1, st)
Proof step 84:
j ≠ 0, i ≤ n→i(# mklist(initial_value(ty), i→n(j))) + i0, 0 ≤ i0 + j, 0 ≤ i0, 0 ≤ j, r -- i ' ∈ addarray(r, ty, ((j = 0 ⊃ []; mklist(initial_value(ty), i→n(j)))) + val ' + mklist(initial_value(ty), i→n(i0)), st), 0 ≤ n→i(# ((j = 0 ⊃ []; mklist(initial_value(ty), i→n(j))))) + i0, 0 ≤ i ⊦ i = j, r -- i ' ∈ addarray(r, ty, i0 + j + 1, st)

Rule argument

[CASEDARG : pos: left 5, ()]

Additional information

[[CONCRETESIMPRULES : ()]]