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Proof step 2 from proof size-less-01 (previous step)

#(s ++ a) < # s ⊦ # s = 0, s = ∅

Heuristic weak cut applied rule cut formula

And closed the goal!

Rule argument

fma: a ∈ s

Additional information

Used simplifier rules: ne-02: ⊦ a ∈ s → (s = ∅ ↔ false);%eq: ⊦ a ∈ s → s ++ a = s;%Size-insert: ⊦ ¬ a ∈ s → #(s ++ a) = # s + 1;%l-02: ⊦ ¬ m + n < m; from specification nat-basic2%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%c: ⊦ m + n = n + m; from specification nat-basic2%ref-1: ⊦ ¬ n < n; from specification nat-basic1 Used formulas: a ∈ s