Nuprl Lemma : face-0_wf
∀[Gamma:j⊢]. (0(𝔽) ∈ {Gamma ⊢ _:𝔽})
Proof
Definitions occuring in Statement :
face-0: 0(𝔽),
face-type: 𝔽,
cubical-term: {X ⊢ _:A},
cubical_set: CubicalSet,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
cubical-term: {X ⊢ _:A},
face-0: 0(𝔽),
subtype_rel: A ⊆r B,
bdd-distributive-lattice: BoundedDistributiveLattice,
lattice-point: Point(l),
record-select: r.x,
face_lattice: face_lattice(I),
face-lattice: face-lattice(T;eq),
free-dist-lattice-with-constraints: free-dist-lattice-with-constraints(T;eq;x.Cs[x]),
constrained-antichain-lattice: constrained-antichain-lattice(T;eq;P),
mk-bounded-distributive-lattice: mk-bounded-distributive-lattice,
mk-bounded-lattice: mk-bounded-lattice(T;m;j;z;o),
record-update: r[x := v],
ifthenelse: if b then t else f fi ,
eq_atom: x =a y,
bfalse: ff,
btrue: tt,
cubical-type-at: A(a),
pi1: fst(t),
face-type: 𝔽,
constant-cubical-type: (X),
I_cube: A(I),
functor-ob: ob(F),
face-presheaf: 𝔽,
all: ∀x:A. B[x],
cubical-type-ap-morph: (u a f),
pi2: snd(t),
cube-set-restriction: f(s),
fl-morph: <f>,
fl-lift: fl-lift(T;eq;L;eqL;f0;f1),
face-lattice-property,
free-dist-lattice-with-constraints-property,
lattice-extend-wc: lattice-extend-wc(L;eq;eqL;f;ac),
lattice-extend: lattice-extend(L;eq;eqL;f;ac),
lattice-fset-join: \/(s),
reduce: reduce(f;k;as),
list_ind: list_ind,
fset-image: f"(s),
f-union: f-union(domeq;rngeq;s;x.g[x]),
list_accum: list_accum,
lattice-0: 0,
empty-fset: {},
nil: [],
it: ⋅
Lemmas referenced :
lattice-0_wf,
face_lattice_wf,
subtype_rel_self,
cubical-type-at_wf_face-type,
I_cube_wf,
fset_wf,
nat_wf,
names-hom_wf,
istype-cubical-type-at,
cube-set-restriction_wf,
face-type_wf,
cubical-type-ap-morph_wf,
cubical_set_wf,
face-lattice-property,
free-dist-lattice-with-constraints-property
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
dependent_set_memberEquality_alt,
lambdaEquality_alt,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
applyEquality,
setElimination,
rename,
inhabitedIsType,
equalityTransitivity,
equalitySymmetry,
sqequalRule,
Error :memTop,
universeIsType,
lambdaFormation_alt,
because_Cache,
functionIsType,
equalityIstype,
instantiate,
axiomEquality
Latex:
\mforall{}[Gamma:j\mvdash{}]. (0(\mBbbF{}) \mmember{} \{Gamma \mvdash{} \_:\mBbbF{}\})
Date html generated:
2020_05_20-PM-02_40_29
Last ObjectModification:
2020_04_04-PM-04_48_24
Theory : cubical!type!theory
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