Nuprl Lemma : context-subset-term-0
∀[Gamma:j⊢]. ∀[T:{Gamma ⊢ _}].  (Top ⊆r {Gamma, 0(𝔽) ⊢ _:T})
Proof
Definitions occuring in Statement : 
context-subset: Gamma, phi
, 
face-0: 0(𝔽)
, 
cubical-term: {X ⊢ _:A}
, 
cubical-type: {X ⊢ _}
, 
cubical_set: CubicalSet
, 
subtype_rel: A ⊆r B
, 
uall: ∀[x:A]. B[x]
, 
top: Top
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
subtype_rel: A ⊆r B
, 
member: t ∈ T
, 
cubical-term: {X ⊢ _:A}
, 
face-0: 0(𝔽)
, 
context-subset: Gamma, phi
, 
all: ∀x:A. B[x]
, 
cubical-term-at: u(a)
, 
bdd-distributive-lattice: BoundedDistributiveLattice
, 
so_lambda: λ2x.t[x]
, 
prop: ℙ
, 
and: P ∧ Q
, 
so_apply: x[s]
, 
uimplies: b supposing a
, 
not: ¬A
, 
implies: P 
⇒ Q
, 
false: False
Lemmas referenced : 
istype-top, 
cubical-type_wf, 
cubical_set_wf, 
I_cube_pair_redex_lemma, 
cube_set_restriction_pair_lemma, 
I_cube_wf, 
lattice-point_wf, 
face_lattice_wf, 
subtype_rel_set, 
bounded-lattice-structure_wf, 
lattice-structure_wf, 
lattice-axioms_wf, 
bounded-lattice-structure-subtype, 
bounded-lattice-axioms_wf, 
equal_wf, 
lattice-meet_wf, 
lattice-join_wf, 
lattice-0_wf, 
lattice-1_wf, 
names-hom_wf, 
fset_wf, 
nat_wf, 
face-lattice-0-not-1
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation_alt, 
lambdaEquality_alt, 
cut, 
introduction, 
extract_by_obid, 
hypothesis, 
universeIsType, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
hypothesisEquality, 
instantiate, 
dependent_set_memberEquality_alt, 
sqequalRule, 
dependent_functionElimination, 
Error :memTop, 
lambdaFormation_alt, 
setIsType, 
equalityIstype, 
applyEquality, 
productEquality, 
cumulativity, 
isectEquality, 
because_Cache, 
independent_isectElimination, 
setElimination, 
rename, 
inhabitedIsType, 
equalityTransitivity, 
equalitySymmetry, 
functionExtensionality, 
independent_functionElimination, 
voidElimination, 
setEquality, 
functionIsType
Latex:
\mforall{}[Gamma:j\mvdash{}].  \mforall{}[T:\{Gamma  \mvdash{}  \_\}].    (Top  \msubseteq{}r  \{Gamma,  0(\mBbbF{})  \mvdash{}  \_:T\})
Date html generated:
2020_05_20-PM-02_57_07
Last ObjectModification:
2020_04_04-PM-05_11_42
Theory : cubical!type!theory
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