Nuprl Lemma : interval-0_wf
∀[Gamma:j⊢]. (0(𝕀) ∈ {Gamma ⊢ _:𝕀})
Proof
Definitions occuring in Statement :
interval-0: 0(𝕀),
interval-type: 𝕀,
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},
interval-0: 0(𝕀),
subtype_rel: A ⊆r B,
lattice-point: Point(l),
record-select: r.x,
dM: dM(I),
free-DeMorgan-algebra: free-DeMorgan-algebra(T;eq),
mk-DeMorgan-algebra: mk-DeMorgan-algebra(L;n),
record-update: r[x := v],
ifthenelse: if b then t else f fi ,
eq_atom: x =a y,
bfalse: ff,
free-DeMorgan-lattice: free-DeMorgan-lattice(T;eq),
free-dist-lattice: free-dist-lattice(T; eq),
mk-bounded-distributive-lattice: mk-bounded-distributive-lattice,
mk-bounded-lattice: mk-bounded-lattice(T;m;j;z;o),
btrue: tt,
cubical-type-at: A(a),
pi1: fst(t),
interval-type: 𝕀,
constant-cubical-type: (X),
I_cube: A(I),
functor-ob: ob(F),
interval-presheaf: 𝕀,
all: ∀x:A. B[x],
dM0: 0,
lattice-0: 0,
empty-fset: {},
nil: [],
it: ⋅,
cubical-type-ap-morph: (u a f),
pi2: snd(t),
cube-set-restriction: f(s),
dM-lift: dM-lift(I;J;f),
free-dma-lift: free-dma-lift(T;eq;dm;eq2;f),
free-DeMorgan-algebra-property,
free-dist-lattice-property,
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
Lemmas referenced :
dM0_wf,
subtype_rel_self,
cubical-type-at_wf,
interval-type_wf,
I_cube_wf,
fset_wf,
nat_wf,
cubical-type-ap-morph_wf,
names-hom_wf,
istype-cubical-type-at,
cube-set-restriction_wf,
cubical_set_wf,
free-DeMorgan-algebra-property,
free-dist-lattice-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,
sqequalRule,
universeIsType,
lambdaFormation_alt,
because_Cache,
instantiate,
inhabitedIsType,
functionIsType,
equalityIstype,
axiomEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[Gamma:j\mvdash{}]. (0(\mBbbI{}) \mmember{} \{Gamma \mvdash{} \_:\mBbbI{}\})
Date html generated:
2020_05_20-PM-02_35_53
Last ObjectModification:
2020_04_04-AM-10_09_58
Theory : cubical!type!theory
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