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Proof step 45 from proof max-rem-notsame (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 46:
m0 < m, bag.max < m, bag.max ≤ m0, ∀ m1. bag.max < m1 → count(m1, bag) = 0 ⊦ bag = ∅, count(m, bag ++ m0) = 0

Rule argument

Additional information

Used simplifier rules: fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat% ⊦ m < n ↔ ¬ n ≤ m; (ss)