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Proof step 10 from proof rmpos-size (previous step)

n = n1 +1, n ≤ # x0, ∀ m, n0. # x0 = m + 1 ∧ n0 ≤ m → #(x0 -p n0) = m ⊦ #((a ' + x0) -p n) = # x0, x0 = []

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 11:
n1 < # x0, ∀ m, n0. # x0 = m + 1 ∧ n0 ≤ m → #(x0 -p n0) = m ⊦ 1 + #(x0 -p n1) = # x0, x0 = []

Rule argument

Additional information

Used simplifier rules: delpos-rec: ⊦ (a ' + x) -p (n + 1) = a + (x -p n);% ⊦ # x = 0 ↔ x = []; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ m + 1 ≤ n ↔ m < n; (s)% ⊦ # a ' = 0 +1; (s)% ⊦ #(x + y) = # x + # y; (s)%a: ⊦ (x + y) + z = x + y + z; from specification list%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ a + x = a ' + x; (s)% ⊦ m +1 = m + 1; (s)