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Proof step 8 from proof ar-elems-append-not-lower-h (previous step)

n0 ≤ # ar1 ⊦ (ar0 + ar1) elems (n0 + # ar0) = (ar0 elems # ar0) ∪ (ar1 elems n0), # ar1 = 0, n0 = 0

User applied rule structural induction

And obtained the following new goals

Proof step 7:
∀ ar1, ar0. n ≤ # ar1 → (ar0 + ar1) elems (n + # ar0) = (ar0 elems # ar0) ∪ (ar1 elems n) ∨ # ar1 = 0 ∨ n = 0, n +1 ≤ # ar1 ⊦ (ar0 + ar1) elems (n +1 + # ar0) = (ar0 elems # ar0) ∪ (ar1 elems n +1), # ar1 = 0, n +1 = 0

Rule argument

[VARWITHVARSEQSARG : n0, ()]

Additional information

[[CONCRETESIMPRULES : ([CSIMPGEN : nat generated by 0, +1;])]]