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Proof step 11 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;% ⊦ ¬ a ∈ x → rmdup(a ' + x) = a + rmdup(x); (s)% ⊦ a + x = a ' + x; (s)%a: ⊦ (x + y) + z = x + y + z; from specification list% ⊦ #(x + y) = # x + # y; (s)% ⊦ # a ' = 0 +1; (s)% ⊦ m + n = m + n0 ↔ n = n0; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ a ∈ x → rmdup(a ' + x) = rmdup(x); (s) Used terms: a0