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Proof step 41 from proof max-rem-notsame (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 42:
m0 < m, bag.max < m, m0 < bag.max, m0 + 1 < m, ∀ m1. bag.max < m1 → count(m1, bag) = 0 ⊦ bag = ∅, count(m, bag ++ m0) = 0

Rule argument

Additional information

Used simplifier rules: ⊦ m +1 = m + 1; (s)% ⊦ m < n → n ≠ 0; (s)%trans: ⊦ n < n0 ∧ n0 < n1 → n < n1; (forward) from specification nat-basic%lf: ⊦ m < n ∧ n < n0 → m +1 < n0; (forward) from specification nat-basic%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic