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Proof step 9 from proof putarray-addarray-override (previous step)

¬ i→n(i) + # vals ≤ # vals0, 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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
# vals0 < i→n(i) + # vals, i + n→i(# vals) ≤ n→i(# vals0), 0 ≤ i ⊦ 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 : ⊦ m < n → n ≠ 0], [CSIMPFORWARD : ⊦ m < n → n ≠ 0], [CSIMPSEQ : ⊦ ¬ m ≤ n ↔ n < m], [CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0])]]