Nuprl Lemma : context-iterated-subset1
∀[X:j⊢]. ∀[xx,yy:{X ⊢ _:𝔽}]. sub_cubical_set{j:l}(X, xx, yy; X, yy)
Proof
Definitions occuring in Statement :
context-subset: Gamma, phi,
face-type: 𝔽,
cubical-term: {X ⊢ _:A},
sub_cubical_set: Y ⊆ X,
cubical_set: CubicalSet,
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
and: P ∧ Q,
cand: A c∧ B,
sub_cubical_set: Y ⊆ X
Lemmas referenced :
sub_cubical_set_transitivity,
context-subset_wf,
face-and_wf,
subset-cubical-term,
context-subset-is-subset,
face-type_wf,
context-iterated-subset,
face-term-implies-subset,
face-term-and-implies1,
cubical-term_wf,
cubical_set_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
applyEquality,
independent_isectElimination,
instantiate,
because_Cache,
sqequalRule,
productElimination,
independent_pairFormation,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
inhabitedIsType,
isect_memberEquality_alt,
isectIsTypeImplies,
universeIsType
Latex:
\mforall{}[X:j\mvdash{}]. \mforall{}[xx,yy:\{X \mvdash{} \_:\mBbbF{}\}]. sub\_cubical\_set\{j:l\}(X, xx, yy; X, yy)
Date html generated:
2020_05_20-PM-02_56_21
Last ObjectModification:
2020_04_04-PM-05_11_16
Theory : cubical!type!theory
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