Nuprl Lemma : sub-cubical-set-true
∀[X:j⊢]. X | I,rho.True ≡ X
Proof
Definitions occuring in Statement :
sub-cubical-set: X | I,rho.P[I; rho],
ext-eq-cs: X ≡ Y,
cubical_set: CubicalSet,
uall: ∀[x:A]. B[x],
true: True
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
cubical_set: CubicalSet,
ext-eq-cs: X ≡ Y,
sub-cubical-set: X | I,rho.P[I; rho],
sub-presheaf-set: X | I,rho.P[I; rho]
Lemmas referenced :
sub-presheaf-set-true,
cube-cat_wf
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isectElimination,
thin,
hypothesis,
sqequalRule
Latex:
\mforall{}[X:j\mvdash{}]. X | I,rho.True \mequiv{} X
Date html generated:
2020_05_20-PM-01_39_39
Last ObjectModification:
2020_04_03-PM-03_32_57
Theory : cubical!type!theory
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