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Proof step 3 from proof union-diff-distr (previous step)

∀ a. count(a, bag1) ≤ count(a, bag0) ⊦ count(a, bag1) ≤ count(a, bag0), (count(a, bag0) - count(a, bag1)) + count(a, bag2) = (count(a, bag1) ≤ count(a, bag0) + count(a, bag2) ⊃ count(a, bag0) + count(a, bag2) - count(a, bag1);0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 4:
count(a, bag0) < count(a, bag1), ∀ a. count(a, bag1) ≤ count(a, bag0) ⊦ (count(a, bag0) - count(a, bag1)) + count(a, bag2) = (count(a, bag1) ≤ count(a, bag0) + count(a, bag2) ⊃ count(a, bag0) + count(a, bag2) - count(a, bag1);0), count(a, bag1) = 0

Rule argument

Additional information

Used simplifier rules: f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic1%lels-01: ⊦ ¬ m ≤ n ↔ n < m; from specification nat