Nuprl Lemma : dM_FL_wf
dM_FL() ∈ 𝕀 j⟶ 𝔽
Proof
Definitions occuring in Statement :
dM_FL: dM_FL(),
face-presheaf: 𝔽,
cube_set_map: A ⟶ B,
interval-presheaf: 𝕀,
member: t ∈ T
Definitions unfolded in proof :
face-presheaf: 𝔽,
interval-presheaf: 𝕀,
cube_set_map: A ⟶ B,
psc_map: A ⟶ B,
nat-trans: nat-trans(C;D;F;G),
all: ∀x:A. B[x],
member: t ∈ T,
type-cat: TypeCat,
cat-arrow: cat-arrow(C),
cube-cat: CubeCat,
op-cat: op-cat(C),
cat-ob: cat-ob(C),
spreadn: spread4,
pi2: snd(t),
pi1: fst(t),
dM_FL: dM_FL(),
compose: f o g,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
DeMorgan-algebra: DeMorganAlgebra,
so_lambda: λ2x.t[x],
prop: ℙ,
and: P ∧ Q,
guard: {T},
uimplies: b supposing a,
so_apply: x[s],
bdd-distributive-lattice: BoundedDistributiveLattice
Lemmas referenced :
ob_pair_lemma,
arrow_pair_lemma,
cat_comp_tuple_lemma,
dM-to-FL_wf,
lattice-point_wf,
dM_wf,
subtype_rel_set,
DeMorgan-algebra-structure_wf,
lattice-structure_wf,
lattice-axioms_wf,
bounded-lattice-structure-subtype,
DeMorgan-algebra-structure-subtype,
subtype_rel_transitivity,
bounded-lattice-structure_wf,
bounded-lattice-axioms_wf,
equal_wf,
lattice-meet_wf,
lattice-join_wf,
DeMorgan-algebra-axioms_wf,
fset_wf,
nat_wf,
fl-morph-comp-dM-lift,
names-hom_wf,
face_lattice_wf,
fl-morph_wf,
dM-lift_wf2
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
sqequalRule,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
Error :memTop,
hypothesis,
dependent_set_memberEquality_alt,
lambdaEquality_alt,
isectElimination,
hypothesisEquality,
universeIsType,
applyEquality,
instantiate,
productEquality,
cumulativity,
because_Cache,
independent_isectElimination,
isectEquality,
lambdaFormation_alt,
functionExtensionality_alt,
inhabitedIsType,
functionIsType,
equalityIstype
Latex:
dM\_FL() \mmember{} \mBbbI{} j{}\mrightarrow{} \mBbbF{}
Date html generated:
2020_05_20-PM-01_45_04
Last ObjectModification:
2020_04_03-PM-04_16_54
Theory : cubical!type!theory
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