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Proof step 12 from proof split-unique-2 (previous step)

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

User applied rule constructor cut

And obtained the following new goals

Proof step 11:
n = m +1, 2^ n * n0 = lead(m0) * 2 * 2^ #fz(m0), odd(n0), ∀ m1, n, n0. m1 < m0 + m0 + 1 → (2^ n * n0 = 2^ #fz(m1) * lead(m1) ∧ odd(n0) → n = #fz(m1) ∧ n0 = lead(m1)) ⊦ n = #fz(m0) + 1 ∧ n0 = lead(m0)

Rule argument

[var-arg: n]

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 : ⊦ m + 1 ≠ 0], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ m + n = n + m], [CSIMPSEQ : ⊦ ¬ odd(2 * m)])]]