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Proof step 23 from proof putarray-addarray-override (previous step)

i→n(i) + # vals ≤ # vals0, 0 ≤ i, i + n→i(# vals) ≤ n→i(# vals0), 0 ≤ i0 ∧ i0 < n→i(# vals0) ∨ i ≤ i0 ∧ i0 < i + n→i(# vals) ⊦ r -- i0 ' ∈ st, ¬ i0 < 0 ∧ ¬ n→i(# vals0) ≤ i0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 11:
0 ≤ i ⊦ n→i(n) ≤ ((* i)) ↔ n ≤ i→n(i)
Proof step 22:
0 ≤ i0, i→n(i) + # vals ≤ # vals0, 0 ≤ i, i + n→i(# vals) ≤ n→i(# vals0), 0 ≤ i0 ∧ i0 < n→i(# vals0) ∨ i ≤ i0 ∧ i0 < i + n→i(# vals) ⊦ r -- i0 ' ∈ st, ¬ i0 < 0 ∧ ¬ # vals0 ≤ i→n(i0)

Rule argument

[speclemmaarg: 0 ≤ i ,n→i(n) ≤ ((* i)) ↔ n ≤ i→n(i) ,[i, n] → [i0, # vals0] ,F ,intnat , ,num-n2i-ls-04 ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : ⊦ i < j → (¬ ¬ j ≤ i ↔ false)], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ i < 0 ∧ 0 ≤ j → i < j], [CSIMPFORWARD : ⊦ i < j ∧ j ≤ j0 → i < j0], [CSIMPFORWARD : ⊦ i ≤ j ∧ j < j0 → i < j0], [CSIMPFORWARD : ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j], [CSIMPFORWARD : ⊦ j < i ∧ i ≤ 0 → j < 0], [CSIMPSEQ : ⊦ i < i + j ↔ 0 < j], [CSIMPSEQ : 0 ≤ i ⊦ ((* i)) < n→i(n) ↔ i→n(i) < n], [CSIMPSEQ : ⊦ 0 < n ↔ n ≠ 0], [CSIMPSEQ : ⊦ # vals = 0 ↔ vals = []], [CSIMPSEQ : ⊦ i ≤ j → (¬ ¬ j < i ↔ false)])], [EXTRATERMS : (i0, # vals0)]]