Nuprl Lemma : sub_cubical_set_weakening

∀[X,Z:j⊢].  sub_cubical_set{j:l}(Z; X) supposing Z = X ∈ CubicalSet{j}


Proof




Definitions occuring in Statement :  sub_cubical_set: Y ⊆ X,  cubical_set: CubicalSet,  uimplies: b supposing a,  uall: ∀[x:A]. B[x],  equal: s = t ∈ T
Definitions unfolded in proof :  uall: ∀[x:A]. B[x],  member: t ∈ T,  cubical_set: CubicalSet,  sub_cubical_set: Y ⊆ X,  sub_ps_context: Y ⊆ X,  cube_set_map: A ⟶ B,  csm-id: 1(X),  pscm-id: 1(X)
Lemmas referenced :  sub_ps_context_weakening,  cube-cat_wf
Rules used in proof :  cut,  introduction,  extract_by_obid,  sqequalHypSubstitution,  sqequalSubstitution,  sqequalTransitivity,  computationStep,  sqequalReflexivity,  isectElimination,  thin,  hypothesis,  sqequalRule

Latex:
\mforall{}[X,Z:j\mvdash{}].    sub\_cubical\_set\{j:l\}(Z;  X)  supposing  Z  =  X



Date html generated: 2020_05_20-PM-01_43_19
Last ObjectModification: 2020_04_03-PM-04_09_49

Theory : cubical!type!theory


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