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Proof step 109 from proof putarray-addarray-01 (previous step)

rk = r0 -- sk, 0 ≤ i, 0 ≤ i0 + n→i(# vals), 0 ≤ i0 + i + n→i(# vals), 0 < i0 ⊦ rk = r -- _length, ( rk ∈ addarray(r, ty, i0 + i + n→i(# vals), st) ∨ r0 = r ∧ is_indexkey(sk) ∧ i ≤ sk .index ∧ sk .index < i + n→i(# vals) ↔ rk ∈ addarray(r, ty, mklist(initial_value(ty), i→n(i)) + vals + mklist(initial_value(ty), i→n(i0)), st)) ∧ (putArray(vals, r, i, addarray(r, ty, i0 + i + n→i(# vals), st))[rk]) = (addarray(r, ty, mklist(initial_value(ty), i→n(i)) + vals + mklist(initial_value(ty), i→n(i0)), st)[rk])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 108:
0 ≤ i, 0 ≤ i0 + n→i(# vals), 0 ≤ i0 + i + n→i(# vals), 0 < i0, r0 ≠ r ∨ sk ≠ _length ⊦ ( r0 -- sk ∈ addarray(r, ty, i0 + i + n→i(# vals), st) ∨ r0 = r ∧ is_indexkey(sk) ∧ i ≤ sk .index ∧ sk .index < i + n→i(# vals) ↔ r0 -- sk ∈ addarray(r, ty, mklist(initial_value(ty), i→n(i)) + vals + mklist(initial_value(ty), i→n(i0)), st)) ∧ (putArray(vals, r, i, addarray(r, ty, i0 + i + n→i(# vals), st))[r0 -- sk]) = (addarray(r, ty, mklist(initial_value(ty), i→n(i)) + vals + mklist(initial_value(ty), i→n(i0)), st)[r0 -- sk])

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ r -- sk = r0 -- sk0 ↔ ¬ ¬ (r = r0 ∧ sk = sk0)])]]