Nuprl Lemma : cubical-type-iso-inverse
∀[X:j⊢]. ((cubical-type-rev-iso(X) o cubical-type-iso(X)) = (λx.x) ∈ (cubical_type{i:l}(X) ⟶ cubical_type{i:l}(X)))
Proof
Definitions occuring in Statement :
cubical-type-rev-iso: cubical-type-rev-iso(X),
cubical-type-iso: cubical-type-iso(X),
cubical_type: cubical_type{i:l}(X),
cubical_set: CubicalSet,
compose: f o g,
uall: ∀[x:A]. B[x],
lambda: λx.A[x],
function: x:A ⟶ B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
cubical_set: CubicalSet,
cubical_type: cubical_type{i:l}(X),
presheaf_type: presheaf_type{i:l}(C; X),
cubes: cubes(X),
cubical-type-rev-iso: cubical-type-rev-iso(X),
presheaf-type-rev-iso: presheaf-type-rev-iso(X),
cubical-type-iso: cubical-type-iso(X),
presheaf-type-iso: presheaf-type-iso(X),
cube-set-restriction: f(s),
psc-restriction: f(s)
Lemmas referenced :
presheaf-type-iso-inverse,
cube-cat_wf
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isectElimination,
thin,
hypothesis,
sqequalRule
Latex:
\mforall{}[X:j\mvdash{}]. ((cubical-type-rev-iso(X) o cubical-type-iso(X)) = (\mlambda{}x.x))
Date html generated:
2020_05_20-PM-01_46_52
Last ObjectModification:
2020_04_03-PM-07_58_21
Theory : cubical!type!theory
Home
Index