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Proof step 94 from proof putarray-addarray-override (previous step)

0 ≤ i, i + n→i(# vals) ≤ n→i(# vals0), i0 < i ∨ n→i(# vals) + i ≤ i0, i0 < 0 ∨ i + n→i(# vals) + n→i(# restn(i→n(i) + # vals, vals0)) ≤ i0 ⊦ (addarray(r0, ty, vals0, st)[r0 -- i0 ']) = st[r0 -- i0 '], ¬ i0 < 0 ∧ ¬ i + n→i(# vals) + n→i(# restn(i→n(i) + # vals, vals0)) ≤ i0, ¬ i0 < 0 ∧ ¬ n→i(# vals0) ≤ i0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 70:
0 ≤ i ⊦ n→i(n) ≤ ((* i)) ↔ n ≤ i→n(i)
Proof step 76:
¬ 0 ≤ i0, 0 ≤ i, i + n→i(# vals) ≤ n→i(# vals0), i0 < i ∨ n→i(# vals) + i ≤ i0, i0 < 0 ∨ i + n→i(# vals) + n→i(# restn(i→n(i) + # vals, vals0)) ≤ i0 ⊦ (addarray(r0, ty, vals0, st)[r0 -- i0 ']) = st[r0 -- i0 '], ¬ i0 < 0 ∧ ¬ i + n→i(# vals) + n→i(# restn(i→n(i) + # vals, vals0)) ≤ i0, ¬ i0 < 0 ∧ ¬ n→i(# vals0) ≤ i0
Proof step 93:
0 ≤ i0, 0 ≤ i, i + n→i(# vals) ≤ n→i(# vals0), i0 < i ∨ n→i(# vals) + i ≤ i0, i0 < 0 ∨ i + n→i(# vals) + n→i(# restn(i→n(i) + # vals, vals0)) ≤ i0 ⊦ (addarray(r0, ty, vals0, st)[r0 -- i0 ']) = st[r0 -- i0 '], ¬ i0 < 0 ∧ ¬ i + n→i(# vals) + n→i(# restn(i→n(i) + # vals, vals0)) ≤ i0, ¬ 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 : ()], [EXTRATERMS : (i0, # vals0)]]