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Proof step 7 from proof subset-smaller (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
count(a0, bag1) < count(a0, bag0), ∀ a0. count(a0, bag0 ++ a) ≤ count(a0, bag1) ⊦

Rule argument

Additional information

Used simplifier rules: ⊦ m < n → n ≠ 0; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ m ≤ n ↔ ¬ n < m; (ss)