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Proof step 4 from proof union-diff-distr (previous step)

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

Heuristic quantifier closing applied rule all left

And closed the goal!

Rule argument

pos: left 2 terms: a

Additional information

Used simplifier rules: add-01: ⊦ n ≤ m → m + n0 - n = (m - n) + n0; from specification nat%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%c: ⊦ m + n = n + m; from specification nat-basic2%lels-01: ⊦ ¬ m ≤ n ↔ n < m; from specification nat%le-ls-simp: ⊦ m ≤ n → (n < m ↔ false); from specification nat%eq-02: n ≤ m ⊦ (m - n) + n0 = n1 ↔ m + n0 = n + n1; from specification nat Used terms: a