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Proof step 7 from proof union-size-not-less-01 (previous step)

m + n < # s0 + # s1, m + n < #(s0 ∪ s1), # s1 ≤ n, # s0 ≤ m, #(s0 ∪ s1) ≤ # s0 + # s1 ⊦ m + n < m + n

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: nat name: fle seq: ⊦ m < n ∧ n ≤ n0 → m < n0 subst: [m, n, n0] → [m + n, # s0 + # s1, m + n] flags: <all paths>

Additional information

Used simplifier rules: ⊦ m + n < m + n0 ↔ n < n0; (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ m ≤ m; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ m + m0 < n + n0 → (m + m0 < n + n0 ↔ true); (ss)% ⊦ n ≤ n0 ∧ n1 ≤ m → n + n1 ≤ n0 + m; (s) Used terms: m + n, # s0 + # s1, m + n