Step
*
1
of Lemma
singleton-orbit
.....set predicate.....
1. T : Type
2. f : T ⟶ T
3. u : T
4. (||[]|| + 1) = 1 ∈ ℤ
5. orbit(T;f;[u])
6. (∀a∈[u].∀n:ℕ. (f^n a ∈ [u]))
⊢ (f u) = u ∈ T
BY
{ (RWO "l_all_cons" (-1) THEN Auto) }
1
1. T : Type
2. f : T ⟶ T
3. u : T
4. (||[]|| + 1) = 1 ∈ ℤ
5. orbit(T;f;[u])
6. ∀n:ℕ. (f^n u ∈ [u])
7. (∀a∈[].∀n:ℕ. (f^n a ∈ [u]))
⊢ (f u) = u ∈ T
Latex:
Latex:
.....set predicate.....
1. T : Type
2. f : T {}\mrightarrow{} T
3. u : T
4. (||[]|| + 1) = 1
5. orbit(T;f;[u])
6. (\mforall{}a\mmember{}[u].\mforall{}n:\mBbbN{}. (f\^{}n a \mmember{} [u]))
\mvdash{} (f u) = u
By
Latex:
(RWO "l\_all\_cons" (-1) THEN Auto)
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