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Proof step 5 from proof del-rmdup-length-nle (previous step)

a ∈ x, # rmdup(x) ≤ # rmdup(x -l a) ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ a ∈ x → # rmdup(x -l a) = # rmdup(x) - 1

Rule argument

spec: inst: name: size-rmdup-del seq: ⊦ a ∈ x → # rmdup(x -l a) = # rmdup(x) - 1 subst: [a, x] → [a, x] flags: rewrite, current

Additional information

Used simplifier rules: lels-01: ⊦ ¬ m ≤ n ↔ n < m; from specification nat%one-01: ⊦ m < 1 ↔ m = 0; from specification nat-basic1%l: ⊦ # x = 0 ↔ x = []; from specification list-data%rm-empty: ⊦ rmdup(x) = [] ↔ x = []; from specification list-dup%in-empty: ⊦ ¬ a ∈ []; from specification list%ls-02: n0 ≤ n ⊦ m ≤ n - n0 ↔ m + n0 ≤ n; from specification nat%succ-01: ⊦ m + 1 ≤ n ↔ m < n; from specification nat%ref-1: ⊦ ¬ n < n; from specification nat-basic1%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%c: ⊦ m + n = n + m; from specification nat-basic2 Used terms: a, x