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Proof step 2 from proof del-size (previous step)

⊦ #(bag -- a) = # bag - (count(a, bag) ≠ 0 ⊃ 1;0)

User applied rule case distinction

And obtained the following new goals

Proof step 3:
count(a, bag) ≠ 0 ⊦ #(bag -- a) = # bag - 1

Rule argument

pos: right 1

Additional information

Used simplifier rules: del-notin: ⊦ count(a, bag) = 0 → bag -- a = bag;%sub-base: ⊦ m - 0 = m; from specification nat