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Proof step 2 from proof union-write-above (previous step)

m ≤ n, m ≤ # asar ⊦ union(asar[n, as], 0, m) = union(asar, 0, m)

User applied rule structural induction

And obtained the following new goals

Proof step 3:
m0 +1 ≤ # asar, m0 +1 ≤ n, ∀ n, asar, as. m0 ≤ n ∧ m0 ≤ # asar → union(asar[n, as], 0, m0) = union(asar, 0, m0) ⊦ union(asar[n, as], 0, m0 +1) = union(asar, 0, m0 +1)

Rule argument

indvar: m

Additional information

Used simplifier rules: union-base: ⊦ union(asar, n, 0) = ∅;%nat freely generated by 0, +1;;