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Proof step 8 from proof finz-bounded-05 (previous step)

n * 2^ n0 ≤ 2 * m0 + 1, 2 * m0 + 2 < 2^ n0 * n + 2^ n0, n0 ≤ #fz(m0) + 1, ∀ m1, n0, n. m1 < m0 + m0 + 1 → (n0 ≤ #fz(m1) ∧ m1 + 1 < 2^ n0 * n + 2^ n0 ∧ n * 2^ n0 ≤ m1 → false) ⊦

User applied rule constructor cut

And obtained the following new goals

Proof step 7:
n0 = m +1, n * 2^ n0 ≤ 2 * m0 + 1, 2 * m0 + 2 < 2^ n0 * n + 2^ n0, n0 ≤ #fz(m0) + 1, ∀ m1, n0, n. m1 < m0 + m0 + 1 → (n0 ≤ #fz(m1) ∧ m1 + 1 < 2^ n0 * n + 2^ n0 ∧ n * 2^ n0 ≤ m1 → false) ⊦

Rule argument

[var-arg: n0]

Additional information

[[CONCRETESIMPRULES : ([CSIMPGEN : nat generated by 0, +1;], [CSIMPSEQ : ⊦ 2^ 0 = 1], [CSIMPSEQ : ⊦ m0 * 1 = m0], [CSIMPSEQ : ⊦ m0 * m * n = (m0 * m) * n], [CSIMPSEQ : ⊦ m * n = n * m], [CSIMPSEQ : n0 < n ⊦ m + ((* n)) < m0 + ((* n0)) ↔ m + (n - n0) < m0], [CSIMPSEQ : ⊦ m + n = n + m], [CSIMPSEQ : ⊦ m ≤ n → (n < m ↔ false)], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1])]]