Nuprl Lemma : discrete-cube_wf
∀[A:Type]. (discrete-cube(A) ∈ CubicalSet)
Proof
Definitions occuring in Statement :
discrete-cube: discrete-cube(A),
cubical-set: CubicalSet,
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
discrete-cube: discrete-cube(A),
cubical-set: CubicalSet,
subtype_rel: A ⊆r B,
top: Top,
and: P ∧ Q,
cand: A c∧ B,
all: ∀x:A. B[x],
compose: f o g,
so_lambda: λ2x.t[x],
so_apply: x[s],
prop: ℙ
Lemmas referenced :
id-morph_wf,
equal-wf-T-base,
compose_wf,
name-comp_wf,
equal_wf,
all_wf,
name-morph_wf,
top_wf,
coordinate_name_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
dependent_set_memberEquality,
dependent_pairEquality,
lambdaEquality,
hypothesisEquality,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
applyEquality,
isect_memberEquality,
voidElimination,
voidEquality,
functionEquality,
lambdaFormation,
functionExtensionality,
independent_pairFormation,
because_Cache,
productElimination,
productEquality,
baseClosed,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
universeEquality
Latex:
\mforall{}[A:Type]. (discrete-cube(A) \mmember{} CubicalSet)
Date html generated:
2016_06_16-PM-05_38_24
Last ObjectModification:
2016_01_18-PM-04_56_56
Theory : cubical!sets
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