Nuprl Lemma : rotate-by-cyclic-map
∀[n,i:ℕ]. rotate-by(n;i) ∈ cyclic-map(ℕn) supposing gcd(i;n) = 1 ∈ ℤ
Proof
Definitions occuring in Statement :
cyclic-map: cyclic-map(T),
rotate-by: rotate-by(n;i),
gcd: gcd(a;b),
int_seg: {i..j-},
nat: ℕ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
member: t ∈ T,
natural_number: $n,
int: ℤ,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
cyclic-map: cyclic-map(T),
prop: ℙ,
all: ∀x:A. B[x],
nat: ℕ,
injection: A →⟶ B,
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
exists: ∃x:A. B[x],
sq_type: SQType(T),
guard: {T},
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
equal_wf,
gcd_wf,
nat_wf,
rotate-by_wf,
rotate-by-injection,
inject_wf,
int_seg_wf,
rotate-by-transitive,
less_than_wf,
subtype_base_sq,
int_subtype_base,
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,
lemma_by_obid,
isectElimination,
thin,
intEquality,
dependent_functionElimination,
setElimination,
rename,
hypothesisEquality,
natural_numberEquality,
isect_memberEquality,
because_Cache,
productElimination,
independent_functionElimination,
lambdaFormation,
dependent_pairFormation,
instantiate,
cumulativity,
independent_isectElimination,
applyEquality,
lambdaEquality
Latex:
\mforall{}[n,i:\mBbbN{}]. rotate-by(n;i) \mmember{} cyclic-map(\mBbbN{}n) supposing gcd(i;n) = 1
Date html generated:
2016_05_15-PM-06_20_34
Last ObjectModification:
2015_12_27-PM-00_05_51
Theory : general
Home
Index