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Proof step 4 from proof size-uni (previous step)

H0 ⊥ H1, ∀ H, H0. # H < # H1 → H0 ⊥ H → #(H0 ∪ H) = # H0 + # H ⊦ #(H0 ∪ H1) = # H0 + # H1

User applied rule cut formula

And obtained the following new goals

Proof step 5:
H0 ⊥ H1, ∀ H, H0. # H < # H1 → H0 ⊥ H → #(H0 ∪ H) = # H0 + # H ⊦ #(H0 ∪ H1) = # H0 + # H1, H1 = ∅

Rule argument

fma: H1 = ∅

Additional information

Used simplifier rules: uni-emp-r: ⊦ H ∪ ∅ = H;%size-emp: ⊦ # ∅ = 0;% ⊦ n + 0 = n; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic Used formulas: H1 = ∅