Nuprl Lemma : count-cyclic-map
∀n:ℕ+. cyclic-map(ℕn) ~ ℕ(n - 1)!
Proof
Definitions occuring in Statement :
cyclic-map: cyclic-map(T),
fact: (n)!,
equipollent: A ~ B,
int_seg: {i..j-},
nat_plus: ℕ+,
all: ∀x:A. B[x],
subtract: n - m,
natural_number: $n
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
nat_plus: ℕ+,
nat: ℕ,
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
not: ¬A,
implies: P ⇒ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
top: Top,
and: P ∧ Q,
prop: ℙ,
subtype_rel: A ⊆r B,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
nat_plus_wf,
cyclic-map_wf,
int_seg_wf,
fact_wf,
subtract_wf,
nat_plus_properties,
decidable__le,
full-omega-unsat,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermSubtract_wf,
itermVar_wf,
intformless_wf,
istype-int,
int_formula_prop_and_lemma,
istype-void,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_subtract_lemma,
int_term_value_var_lemma,
int_formula_prop_less_lemma,
int_formula_prop_wf,
le_wf,
combination_wf,
injection_wf,
equipollent_same,
equipollent_functionality_wrt_equipollent,
equipollent_transitivity,
equipollent_inversion,
cyclic-map-equipollent,
injections-combinations,
equipollent-factorial,
equipollent_weakening_ext-eq,
ext-eq_weakening
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation_alt,
universeIsType,
cut,
introduction,
extract_by_obid,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
natural_numberEquality,
setElimination,
rename,
hypothesisEquality,
dependent_set_memberEquality_alt,
because_Cache,
dependent_functionElimination,
unionElimination,
independent_isectElimination,
approximateComputation,
independent_functionElimination,
dependent_pairFormation_alt,
lambdaEquality_alt,
int_eqEquality,
isect_memberEquality_alt,
voidElimination,
sqequalRule,
independent_pairFormation,
applyEquality,
productElimination
Latex:
\mforall{}n:\mBbbN{}\msupplus{}. cyclic-map(\mBbbN{}n) \msim{} \mBbbN{}(n - 1)!
Date html generated:
2019_10_15-AM-11_22_24
Last ObjectModification:
2018_10_09-PM-00_15_12
Theory : general
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