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

∀ bag1. #(bag ∪ bag1) = # bag + # bag1 ⊦ #((bag ++ a) ∪ bag1) = #(bag ++ a) + # bag1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: union-rec: ⊦ (bag0 ++ a) ∪ bag1 = (bag0 ∪ bag1) ++ a;%union-ass: ⊦ bag0 ∪ bag1 ∪ bag2 = (bag0 ∪ bag1) ∪ bag2;%union-com: ⊦ bag0 ∪ bag1 = bag1 ∪ bag0;%size-rec: ⊦ #(bag ++ a) = # bag + 1;%c: ⊦ m + n = n + m; from specification nat-basic2%eq-01: ⊦ m + n = m + n0 ↔ n = n0; from specification nat-basic2%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2