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Proof step 2 from proof subset-trans (previous step)

bag0 ⊆ bag1, bag1 ⊆ bag2 ⊦ bag0 ⊆ bag2

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
count(a, bag2) < count(a, bag0), ∀ a. count(a, bag0) ≤ count(a, bag1), ∀ a. count(a, bag1) ≤ count(a, bag2) ⊦

Rule argument

Additional information

Used simplifier rules: count-subset: ⊦ bag0 ⊆ bag1 ↔ (∀ a. count(a, bag0) ≤ count(a, bag1));% ⊦ m < n → n ≠ 0; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ m ≤ n ↔ ¬ n < m; (ss)