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Proof step 13 from proof subset-plusplus (previous step)

a0 = a, count(a0, bag1 ++ a) < count(a0, bag0 ++ a), ∀ a. count(a, bag0) ≤ count(a, bag1) ⊦

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 14:
count(a, bag1) < count(a, bag0), ∀ a. count(a, bag0) ≤ count(a, bag1) ⊦

Rule argument

Additional information

Used simplifier rules: ⊦ m < n → n ≠ 0; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m + n < m + n0 ↔ n < n0; (s)% ⊦ count(a, bag ++ a) = count(a, bag) + 1; (s)