Nuprl Lemma : residues-mod_wf
∀[n:ℕ]. (residues-mod(n) ∈ residue(n) List)
Proof
Definitions occuring in Statement :
residues-mod: residues-mod(n),
residue: residue(n),
list: T List,
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
residues-mod: residues-mod(n),
nat: ℕ,
all: ∀x:A. B[x],
int_seg: {i..j-},
subtype_rel: A ⊆r B,
prop: ℙ,
uimplies: b supposing a,
residue: residue(n),
uiff: uiff(P;Q),
and: P ∧ Q,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
guard: {T}
Lemmas referenced :
nat_wf,
filter_type,
int_seg_wf,
eq_int_wf,
gcd_wf,
upto_wf,
subtype_rel_list,
assert_wf,
residue_wf,
assert_of_eq_int,
coprime_elim_a,
coprime_wf,
assoced_weakening
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
hypothesis,
sqequalRule,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
lemma_by_obid,
isectElimination,
thin,
natural_numberEquality,
setElimination,
rename,
hypothesisEquality,
lambdaEquality,
dependent_functionElimination,
applyEquality,
setEquality,
independent_isectElimination,
productElimination,
dependent_set_memberEquality,
independent_functionElimination
Latex:
\mforall{}[n:\mBbbN{}]. (residues-mod(n) \mmember{} residue(n) List)
Date html generated:
2016_05_15-PM-07_30_50
Last ObjectModification:
2015_12_27-AM-11_19_37
Theory : general
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