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Proof step 10 from proof size-rmdup-del (previous step)

# rmdup(x0) = m0 + 1, # rmdup(a0 ' + x0) = m + 1, ∀ a. a ∈ x0 → # rmdup(x0 -l a) = m0 ⊦ # rmdup(x0 -l a0) = m, x0 = []

User applied rule all left

And closed the goal!

Rule argument

pos: left 3 terms: a0 abort: F discard: F computed: T

Additional information

Used simplifier rules: in-03: ⊦ ¬ a ∈ x → x -l a = x;%rmdup-n: ⊦ ¬ a ∈ x → rmdup(a ' + x) = a + rmdup(x); from specification list-dup%c: ⊦ a + x = a ' + x; from specification list%a: ⊦ (x + y) + z = x + y + z; from specification list%len: ⊦ #(x + y) = # x + # y; from specification list%len-02: ⊦ # a ' = 0 +1; from specification list%eq-01: ⊦ m + n = m + n0 ↔ n = n0; from specification nat-basic2%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%c: ⊦ m + n = n + m; from specification nat-basic2%rmdup-y: ⊦ a ∈ x → rmdup(a ' + x) = rmdup(x); from specification list-dup Used terms: a0