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Proof step 201 from proof addarray-put-01 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 200:
0 ≤ i0 + j, 0 ≤ i0, 0 ≤ j ⊦ ( rk ∈ (addarray(r, ty, i0 + j + 1, st)[r -- j ', val]) ↔ rk ∈ addarray(r, ty, ((j = 0 ⊃ []; mklist(initial_value(ty), i→n(j)))) + val ' + mklist(initial_value(ty), i→n(i0)), st)) ∧ (addarray(r, ty, i0 + j + 1, st)[r -- j ', val][rk]) = (addarray(r, ty, ((j = 0 ⊃ []; mklist(initial_value(ty), i→n(j)))) + val ' + mklist(initial_value(ty), i→n(i0)), st)[rk])

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ()]]