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Proof step 2 from proof del-rmdup-length-nle (previous step)

# rmdup(a ' + x) ≤ # rmdup(x -l a) ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ ¬ a ∈ x → rmdup(a ' + x) = a + rmdup(x)
Proof step 4:
¬ ¬ a ∈ x, # rmdup(a ' + x) ≤ # rmdup(x -l a) ⊦

Rule argument

spec: list-dup inst: name: rmdup-n seq: ⊦ ¬ a ∈ x → rmdup(a ' + x) = a + rmdup(x) subst: [x, a] → [x, a] flags: rewrite

Additional information

Used simplifier rules: in-03: ⊦ ¬ a ∈ x → x -l a = x;%c: ⊦ a + x = a ' + x; from specification list%len-05: ⊦ #(a ' + x) = (# x)+1; from specification list%succ: ⊦ m +1 = m + 1; from specification nat-basic2%a: ⊦ (x + y) + z = x + y + z; from specification list%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: x, a