Nuprl Lemma : unit-cube-map_wf
∀[I,J:Cname List]. ∀[f:name-morph(I;J)]. (unit-cube-map(f) ∈ unit-cube(J) ⟶ unit-cube(I))
Proof
Definitions occuring in Statement :
unit-cube-map: unit-cube-map(f),
unit-cube: unit-cube(I),
cube-set-map: A ⟶ B,
name-morph: name-morph(I;J),
coordinate_name: Cname,
list: T List,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
unit-cube-map: unit-cube-map(f),
member: t ∈ T,
unit-cube: unit-cube(I),
type-cat: TypeCat,
cat-arrow: cat-arrow(C),
name-cat: NameCat,
cat-ob: cat-ob(C),
pi1: fst(t),
pi2: snd(t),
all: ∀x:A. B[x],
top: Top,
cat-comp: cat-comp(C),
compose: f o g,
cube-set-map: A ⟶ B,
nat-trans: nat-trans(C;D;F;G)
Lemmas referenced :
name-morph_wf,
list_wf,
coordinate_name_wf,
ob_pair_lemma,
istype-void,
name-comp_wf,
arrow_pair_lemma,
name-comp-assoc,
cat-ob_wf,
name-cat_wf,
cat-arrow_wf,
type-cat_wf,
cat-comp_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
universeIsType,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
inhabitedIsType,
sqequalRule,
dependent_functionElimination,
isect_memberEquality_alt,
voidElimination,
lambdaEquality_alt,
because_Cache,
lambdaFormation_alt,
functionExtensionality_alt,
dependent_set_memberEquality_alt,
functionIsType,
applyEquality,
equalityIstype,
instantiate
Latex:
\mforall{}[I,J:Cname List]. \mforall{}[f:name-morph(I;J)]. (unit-cube-map(f) \mmember{} unit-cube(J) {}\mrightarrow{} unit-cube(I))
Date html generated:
2019_11_05-PM-00_26_00
Last ObjectModification:
2018_12_10-AM-09_54_01
Theory : cubical!sets
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