Nuprl Lemma : face-1-implies-subset
∀[Gamma:j⊢]. ∀[phi:{Gamma ⊢ _:𝔽}]. sub_cubical_set{j:l}(Gamma; Gamma, phi) supposing Gamma ⊢ (1(𝔽) ⇒ phi)
Proof
Definitions occuring in Statement :
face-term-implies: Gamma ⊢ (phi ⇒ psi),
context-subset: Gamma, phi,
face-1: 1(𝔽),
face-type: 𝔽,
cubical-term: {X ⊢ _:A},
sub_cubical_set: Y ⊆ X,
cubical_set: CubicalSet,
uimplies: b supposing a,
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
and: P ∧ Q,
cand: A c∧ B,
sub_cubical_set: Y ⊆ X,
prop: ℙ
Lemmas referenced :
sub_cubical_set_transitivity,
context-subset_wf,
face-1_wf,
context-1-subset,
face-term-implies_wf,
cubical-term_wf,
face-type_wf,
cubical_set_wf,
face-term-implies-subset
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
independent_isectElimination,
instantiate,
independent_pairFormation,
sqequalRule,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
universeIsType,
isect_memberEquality_alt,
isectIsTypeImplies,
inhabitedIsType
Latex:
\mforall{}[Gamma:j\mvdash{}]. \mforall{}[phi:\{Gamma \mvdash{} \_:\mBbbF{}\}].
sub\_cubical\_set\{j:l\}(Gamma; Gamma, phi) supposing Gamma \mvdash{} (1(\mBbbF{}) {}\mRightarrow{} phi)
Date html generated:
2020_05_20-PM-02_54_07
Last ObjectModification:
2020_04_04-PM-05_08_31
Theory : cubical!type!theory
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