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Proof step 7 from proof rmpos-size (previous step)

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

Heuristic cut applied rule cut formula

And obtained the following new goals

Proof step 8:
n ≤ # x0, ∀ m, n. # x0 = m + 1 ∧ n ≤ m → #(x0 -p n) = m ∨ x0 = [] ⊦ #((a ' + x0) -p n) = # x0, x0 = []

Rule argument

fma: x0 = []

Additional information

Used simplifier rules: delnr-one: ⊦ a ' -p 0 = [];% ⊦ x + [] = x; (s)%a: ⊦ (x + y) + z = x + y + z; from specification list% ⊦ # [] = 0; (s)% ⊦ # x = 0 ↔ x = []; (s)% ⊦ m ≤ 0 ↔ m = 0; (s)% ⊦ m + 1 ≠ 0; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic Used formulas: x0 = []