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Proof step 6 from proof finz-bounded-05 (previous step)

m ≤ #fz(m0), m0 + 1 < 2^ m * n + 2^ m, 2^ m * n ≤ m0, ∀ 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 apply induction

And closed the goal!

Rule argument

[substlist-arg: [m1, n0, n] → [m0, m, n]]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ m + m0 < n + n0 → (¬ m + m0 < n + n0 ↔ false)], [CSIMPSEQ : ⊦ m * n = n * m], [CSIMPSEQ : ⊦ m + m = 2 * m], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ m + n = n + m], [CSIMPSEQ : ⊦ m < n + 1 ↔ ¬ n < m], [CSIMPSEQ : ⊦ ¬ 2 * n < n], [CSIMPSEQ : ⊦ m0 * m * n = (m0 * m) * n])], [EXTRATERMS : (m0, m, n)]]