Nuprl Lemma : cubical-type-at_wf_face-type
∀[J:fset(ℕ)]. ∀[rho:Top]. (𝔽(rho) ∈ Type)
Proof
Definitions occuring in Statement :
face-type: 𝔽,
cubical-type-at: A(a),
fset: fset(T),
nat: ℕ,
uall: ∀[x:A]. B[x],
top: Top,
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
face-type: 𝔽,
cubical-type-at: A(a),
face-presheaf: 𝔽,
constant-cubical-type: (X),
pi1: fst(t),
all: ∀x:A. B[x],
top: Top,
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,
uall_wf,
equal_wf,
lattice-meet_wf,
lattice-join_wf,
top_wf,
fset_wf,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis,
isectElimination,
hypothesisEquality,
applyEquality,
instantiate,
lambdaEquality,
productEquality,
cumulativity,
universeEquality,
because_Cache,
independent_isectElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[J:fset(\mBbbN{})]. \mforall{}[rho:Top]. (\mBbbF{}(rho) \mmember{} Type)
Date html generated:
2018_05_23-AM-09_19_47
Last ObjectModification:
2017_11_10-AM-11_39_47
Theory : cubical!type!theory
Home
Index