Nuprl Lemma : uniform-comp-function-cumulativity
∀[Gamma:j⊢]. ∀[A:{Gamma ⊢ _}]. ∀[comp:composition-function{[i | j]:l, i:l}(Gamma; A)].
(uniform-comp-function{[i | j]:l, i:l}(Gamma; A; comp) ⇒ uniform-comp-function{j:l, i:l}(Gamma; A; comp))
Proof
Definitions occuring in Statement :
uniform-comp-function: uniform-comp-function{j:l, i:l}(Gamma; A; comp),
composition-function: composition-function{j:l,i:l}(Gamma;A),
cubical-type: {X ⊢ _},
cubical_set: CubicalSet,
uall: ∀[x:A]. B[x],
implies: P ⇒ Q
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
implies: P ⇒ Q,
uniform-comp-function: uniform-comp-function{j:l, i:l}(Gamma; A; comp),
all: ∀x:A. B[x],
subtype_rel: A ⊆r B,
prop: ℙ
Lemmas referenced :
cubical_set_cumulativity-i-j,
cube_set_map_cumulativity-i-j,
cube-context-adjoin_wf,
interval-type_wf,
cube_set_map_wf,
uniform-comp-function_wf,
composition-function_wf,
cubical-type_wf,
cubical_set_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
lambdaFormation_alt,
sqequalHypSubstitution,
hypothesis,
dependent_functionElimination,
thin,
hypothesisEquality,
applyEquality,
instantiate,
extract_by_obid,
sqequalRule,
isectElimination,
universeIsType,
because_Cache,
inhabitedIsType,
lambdaEquality_alt,
axiomEquality,
functionIsTypeImplies,
isect_memberEquality_alt,
isectIsTypeImplies
Latex:
\mforall{}[Gamma:j\mvdash{}]. \mforall{}[A:\{Gamma \mvdash{} \_\}]. \mforall{}[comp:composition-function\{[i | j]:l, i:l\}(Gamma; A)].
(uniform-comp-function\{[i | j]:l, i:l\}(Gamma; A; comp)
{}\mRightarrow{} uniform-comp-function\{j:l, i:l\}(Gamma; A; comp))
Date html generated:
2020_05_20-PM-04_21_50
Last ObjectModification:
2020_04_21-PM-08_42_08
Theory : cubical!type!theory
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