Nuprl Lemma : face_lattice-point_wf
∀[I:fset(ℕ)]. (Point(face_lattice(I)) ∈ Type)
Proof
Definitions occuring in Statement :
face_lattice: face_lattice(I),
fset: fset(T),
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type,
lattice-point: Point(l)
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
bdd-distributive-lattice: BoundedDistributiveLattice,
so_lambda: λ2x.t[x],
prop: ℙ,
and: P ∧ Q,
so_apply: x[s],
uimplies: b supposing a
Lemmas referenced :
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,
fset_wf,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
applyEquality,
sqequalRule,
instantiate,
lambdaEquality_alt,
productEquality,
cumulativity,
isectEquality,
because_Cache,
universeIsType,
independent_isectElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[I:fset(\mBbbN{})]. (Point(face\_lattice(I)) \mmember{} Type)
Date html generated:
2020_05_20-PM-01_44_15
Last ObjectModification:
2020_04_05-PM-01_40_44
Theory : cubical!type!theory
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