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Proof step 4 from proof ext-rec (previous step)

∀ b. count(b, bag1) = (a = b ⊃ 1;0) + count(b, bag0) ⊦ ∀ a0. count(a0, bag1) = count(a0, bag0 ++ a)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
∀ b. count(b, bag1) = (a = b ⊃ 1;0) + count(b, bag0) ⊦ count(a0, bag1) = (a0 = a ⊃ 1;0) + count(a0, bag0)

Rule argument

Additional information

Used simplifier rules: count-insert: ⊦ count(a, bag ++ b) = (a = b ⊃ 1;0) + count(a, bag);