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Proof step 25 from proof putarray-addarray-override (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
n ≤ # vals ⊦ # restn(n, vals) = # vals - n
Proof step 9:
¬ 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
Proof step 24:
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(# vals0 - i→n(i) + # vals) ≤ i0

Rule argument

[speclemmaarg: n ≤ # vals ,# restn(n, vals) = # vals - n ,[vals, n] → [vals0, i→n(i) + # vals] ,F ,list-del ,javavalues ,rest-len ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (vals0, i→n(i) + # vals)]]