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Proof step 26 from proof addarray-addaray (previous step)

sk = i0 ', 0 ≤ i, is_indexkey(sk), i0 < i, 0 ≤ i0, 0 < i ⊦ (r -- sk ∈ addarray(r, ty, i, st) ↔ r -- sk ∈ addarray(r, ty, mklist(initial_value(ty), i→n(i)), st)) ∧ (addarray(r, ty, i, st)[r -- sk]) = (addarray(r, ty, mklist(initial_value(ty), i→n(i)), st)[r -- sk])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 18:
⊦ 0 ≤ j ∧ j < i → r -- j ' ∈ addarray(r, ty, i, st)
Proof step 19:
⊦ r -- j ' ∈ addarray(r, ty, vals, st) ↔ r -- j ' ∈ st ∨ 0 ≤ j ∧ j < n→i(# vals)
Proof step 20:
⊦ 0 ≤ j ∧ j < i → (addarray(r, ty, i, st)[r -- j ']) = initial_value(ty)
Proof step 25:
0 ≤ i, i0 < i, 0 < i, 0 ≤ i0 ⊦ initial_value(ty) = (addarray(r, ty, mklist(initial_value(ty), i→n(i)), st)[r -- i0 '])

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPFORWARD : ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j], [CSIMPSEQ : ⊦ i < j → (¬ ¬ j ≤ i ↔ false)], [CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ 0 < i → n→i(i→n(i)) = i], [CSIMPSEQ : ⊦ # mklist(val, n) = n], [CSIMPSEQ : ⊦ i ≤ j → (¬ ¬ j < i ↔ false)], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : ⊦ is_indexkey(i ')])]]