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Proof step 48 from proof max-rem-notsame (previous step)

bag.max < m, m0 < m, bag.max ≤ m0, ∀ m1. bag.max < m1 → count(m1, bag) = 0 ⊦ (m = m0 ⊃ 1;0) + count(m, bag) = 0, bag = ∅

Heuristic quantifier closing applied rule all left

And closed the goal!

Rule argument

pos: left 4 terms: m

Additional information

Used simplifier rules: ⊦ m + n = 0 ↔ m = 0 ∧ n = 0; (ws)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic% ⊦ m < n → ¬ n < m; (s) Used terms: m