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Proof step 9 from proof subset-smaller (previous step)

count(a0, bag1) < count(a0, bag0), count(a0, bag0 ++ a) ≤ count(a0, bag1), ∀ a0. count(a0, bag0 ++ a) ≤ count(a0, bag1) ⊦

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 10:
count(a0, bag1) < count(a0, bag0), count(a0, bag0 ++ a) < count(a0, bag0), count(a0, bag0 ++ a) ≤ count(a0, bag1), ∀ a0. count(a0, bag0 ++ a) ≤ count(a0, bag1) ⊦

Rule argument

Additional information

Used simplifier rules: fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat