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Proof step 8 from proof rmpos-size (previous step)

n ≤ # x0, ∀ m, n0. # x0 = m + 1 ∧ n0 ≤ m → #(x0 -1l n0) = m ⊦ x0 = [], #((a ' + x0) -1l n) = # x0

User applied rule constructor cut

And obtained the following new goals

Proof step 9:
n = n1 +1, n ≤ # x0, ∀ m, n0. # x0 = m + 1 ∧ n0 ≤ m → #(x0 -1l n0) = m ⊦ x0 = [], #((a ' + x0) -1l n) = # x0

Rule argument

var: n

Additional information

Used simplifier rules: delpos-base: ⊦ (a ' + x) -1l 0 = x;%nat freely generated by 0, +1;;%a: ⊦ (x + y) + z = x + y + z; from specification list