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Proof step 6 from proof bag-add2-eq-elim (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
∀ a0. (a0 = b ⊃ 1;0) + count(a0, bag0) = count(a0, bag1) ⊦ (a = b ⊃ 1;0) + count(a, bag0) = count(a, bag1)

Rule argument

Additional information

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