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Proof step 9 from proof size-del-nodups (previous step)

a ∈ x0, ∀ m, a1. # x0 = m + 1 ∧ a1 ∈ x0 → #(x0 -l a1) = m ⊦ 1 + #(x0 -l a) = # x0, x0 = [], dups(x0), a0 ∈ x0

User applied rule all left

And closed the goal!

Rule argument

pos: left 2 terms: # x0 - 1, a abort: F discard: T computed: F

Additional information

Used simplifier rules: ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ m < 1 ↔ m = 0; (s)% ⊦ # x = 0 ↔ x = []; (s)%n ≤ m ⊦ (m - n) + n0 = n1 ↔ m + n0 = n + n1; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic Used terms: # x0 - 1, a