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Proof step 5 from proof rmtoobigpos (previous step)

n = n0 +1, # x0 < n, ∀ n. # x0 ≤ n → x0 -1l n = x0 ⊦ (a ' + x0) -1l n = a ' + x0, n = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
# x0 ≤ n0, ∀ n. # x0 ≤ n → x0 -1l n = x0 ⊦ x0 -1l n0 = x0

Rule argument

Additional information

Used simplifier rules: delpos-rec: ⊦ (a ' + x) -1l (n + 1) = a + (x -1l n);%lels: ⊦ ¬ m < n ↔ n ≤ m; from specification nat%s: ⊦ m < n + 1 ↔ ¬ n < m; from specification nat-basic2%oz: ⊦ m + 1 ≠ 0; from specification nat-basic2%app-08: ⊦ a ' + x = a ' + y ↔ x = y; from specification list%a: ⊦ (x + y) + z = x + y + z; from specification list%c: ⊦ m + n = n + m; from specification nat-basic2%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%c: ⊦ a + x = a ' + x; from specification list%succ: ⊦ m +1 = m + 1; from specification nat-basic2