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Proof step 26 from proof putarray-addarray-override (previous step)

¬ r0 ≠ r, 0 ≤ i, i + n→i(# vals) ≤ n→i(# vals0) ⊦ r0 -- i0 ' ∈ addarray(r, ty, vals0, st) ∨ r0 = r ∧ i ≤ i0 ∧ i0 < i + n→i(# vals) ↔ r0 -- i0 ' ∈ addarray(r, ty, firstn(i→n(i), vals0) + vals + restn(i→n(i) + # vals, vals0), st)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 4:
⊦ r -- j ' ∈ addarray(r, ty, vals, st) ↔ r -- j ' ∈ st ∨ 0 ≤ j ∧ j < n→i(# vals)
Proof step 25:
0 ≤ i, i + n→i(# vals) ≤ n→i(# vals0) ⊦ r -- i0 ' ∈ addarray(r, ty, vals0, st) ∨ i ≤ i0 ∧ i0 < i + n→i(# vals) ↔ r -- i0 ' ∈ st ∨ ¬ i0 < 0 ∧ ¬ i + n→i(# vals) + n→i(# restn(i→n(i) + # vals, vals0)) ≤ i0

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ m + n = n + m], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ 0 ≤ i → n→i(i→n(i)) = i], [CSIMPSEQ : ⊦ n→i(m + n) = n→i(m) + n→i(n)], [CSIMPSEQ : ⊦ (vals + vals0) + vals1 = vals + vals0 + vals1], [CSIMPSEQ : ⊦ # firstn(n, vals) = n], [CSIMPSEQ : ⊦ # (vals + vals0) = # vals + # vals0], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0])]]