Nuprl Lemma : cycle_wf2
∀[n:ℕ]. ∀[L:Combination(n;ℕn)]. (cycle(L) ∈ cyclic-map(ℕn))
Proof
Definitions occuring in Statement :
cyclic-map: cyclic-map(T),
combination: Combination(n;T),
cycle: cycle(L),
int_seg: {i..j-},
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
natural_number: $n
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
cyclic-map: cyclic-map(T),
nat: ℕ,
combination: Combination(n;T),
injection: A →⟶ B,
and: P ∧ Q,
uimplies: b supposing a,
prop: ℙ,
all: ∀x:A. B[x],
no_repeats: no_repeats(T;l),
so_lambda: λ2x.t[x],
guard: {T},
int_seg: {i..j-},
ge: i ≥ j ,
lelt: i ≤ j < k,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
implies: P ⇒ Q,
not: ¬A,
top: Top,
so_apply: x[s],
sq_stable: SqStable(P),
squash: ↓T,
uiff: uiff(P;Q),
sq_type: SQType(T),
surject: Surj(A;B;f),
l_member: (x ∈ l),
subtype_rel: A ⊆r B,
le: A ≤ B,
less_than': less_than'(a;b),
cand: A c∧ B
Lemmas referenced :
combination_wf,
int_seg_wf,
nat_wf,
cycle_wf,
cycle-injection,
inject_wf,
uall_wf,
isect_wf,
less_than_wf,
not_wf,
equal_wf,
select_wf,
nat_properties,
int_seg_properties,
decidable__le,
satisfiable-full-omega-tt,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_wf,
length_wf,
squash_wf,
sq_stable__and,
sq_stable__uall,
sq_stable__not,
sq_stable__equal,
no_repeats_wf,
list_wf,
no_repeats_inject,
subtype_base_sq,
int_subtype_base,
injection-is-surjection,
decidable__lt,
intformless_wf,
intformeq_wf,
int_formula_prop_less_lemma,
int_formula_prop_eq_lemma,
int_seg_subtype_nat,
false_wf,
set_subtype_base,
lelt_wf,
cycle-transitive,
fun_exp_wf,
all_wf,
exists_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
dependent_set_memberEquality,
sqequalHypSubstitution,
hypothesis,
sqequalRule,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
extract_by_obid,
isectElimination,
thin,
natural_numberEquality,
setElimination,
rename,
hypothesisEquality,
because_Cache,
isect_memberEquality,
productElimination,
independent_isectElimination,
functionExtensionality,
applyEquality,
lambdaFormation,
lambdaEquality,
dependent_functionElimination,
unionElimination,
dependent_pairFormation,
int_eqEquality,
intEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
independent_functionElimination,
imageMemberEquality,
baseClosed,
imageElimination,
productEquality,
instantiate,
cumulativity,
applyLambdaEquality,
comment
Latex:
\mforall{}[n:\mBbbN{}]. \mforall{}[L:Combination(n;\mBbbN{}n)]. (cycle(L) \mmember{} cyclic-map(\mBbbN{}n))
Date html generated:
2018_05_21-PM-08_25_59
Last ObjectModification:
2017_07_26-PM-05_54_19
Theory : general
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