Nuprl Lemma : poset-functor-id
∀[I:Cname List]. ∀[f:name-morph(I;I)].
poset-functor(I;I;f) = 1 ∈ Functor(poset-cat(I);poset-cat(I)) supposing f = 1 ∈ name-morph(I;I)
Proof
Definitions occuring in Statement :
poset-functor: poset-functor(J;K;f),
poset-cat: poset-cat(J),
id-morph: 1,
name-morph: name-morph(I;J),
coordinate_name: Cname,
id_functor: 1,
cat-functor: Functor(C1;C2),
list: T List,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
squash: ↓T,
prop: ℙ,
true: True,
subtype_rel: A ⊆r B,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q
Lemmas referenced :
equal_wf,
squash_wf,
true_wf,
cat-functor_wf,
poset-cat_wf,
poset-id-functor,
id_functor_wf,
iff_weakening_equal,
equal-wf-T-base,
poset-functor_wf,
name-morph_wf,
id-morph_wf,
list_wf,
coordinate_name_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
hypothesis,
thin,
applyEquality,
lambdaEquality,
sqequalHypSubstitution,
imageElimination,
extract_by_obid,
isectElimination,
hypothesisEquality,
equalityTransitivity,
equalitySymmetry,
universeEquality,
because_Cache,
natural_numberEquality,
sqequalRule,
imageMemberEquality,
baseClosed,
independent_isectElimination,
productElimination,
independent_functionElimination,
hyp_replacement,
applyLambdaEquality,
isect_memberEquality,
axiomEquality
Latex:
\mforall{}[I:Cname List]. \mforall{}[f:name-morph(I;I)]. poset-functor(I;I;f) = 1 supposing f = 1
Date html generated:
2017_10_05-AM-10_29_19
Last ObjectModification:
2017_07_28-AM-11_24_11
Theory : cubical!sets
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