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Proof step 3 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 4:
⊦ ¬ a ∈ x → rmdup(a ' + x) = a + rmdup(x)
Proof step 5:
a ∈ x, # rmdup(a ' + x) ≤ # rmdup(x -l a) ⊦

Rule argument

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

Additional information

Used simplifier rules: in-03: ⊦ ¬ a ∈ x → x -l a = x;% ⊦ a + x = a ' + x; (s)% ⊦ #(x + y) = # x + # y; (s)% ⊦ # a ' = 0 +1; (s)%a: ⊦ (x + y) + z = x + y + z; from specification list% ⊦ m + m0 ≤ m ↔ m0 = 0; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic Used terms: x, a