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Proof step 4 from proof difference (previous step)

⊦ count(a, bag0 \ bag1) = (count(a, bag1) < count(a, bag0) ⊃ count(a, bag0) - count(a, bag1);0)

User applied rule structural induction

And obtained the following new goals

Proof step 5:
⊦ count(a, bag0 \ ∅) = (count(a, ∅) < count(a, bag0) ⊃ count(a, bag0) - count(a, ∅);0)
Proof step 7:
∀ a, bag0. count(a, bag0 \ bag) = (count(a, bag) < count(a, bag0) ⊃ count(a, bag0) - count(a, bag);0) ⊦ count(a, bag0 \ (bag ++ a0)) = (count(a, bag ++ a0) < count(a, bag0) ⊃ count(a, bag0) - count(a, bag ++ a0);0)

Rule argument

indvar: bag1

Additional information

Used simplifier rules: bag generated by ∅, ++;;