Nuprl Lemma : compatible-system_wf

āˆ€[Gamma:jāŠ¢]. āˆ€[sys:(phi:{Gamma āŠ¢ _:š”½} Ć— {Gamma, phi āŠ¢ _}) List].  (compatible-system{i:l}(Gamma;sys) āˆˆ ā„™{[i' j']})


Proof




Definitions occuring in Statement :  compatible-system: compatible-system{i:l}(Gamma;sys) context-subset: Gamma, phi face-type: š”½ cubical-term: {X āŠ¢ _:A} cubical-type: {X āŠ¢ _} cubical_set: CubicalSet list: List uall: āˆ€[x:A]. B[x] prop: ā„™ member: t āˆˆ T product: x:A Ć— B[x]
Definitions unfolded in proof :  uall: āˆ€[x:A]. B[x] member: t āˆˆ T compatible-system: compatible-system{i:l}(Gamma;sys) so_lambda: Ī»2y.t[x; y] subtype_rel: A āŠ†B uimplies: supposing a so_apply: x[s1;s2]
Lemmas referenced :  pairwise_wf2 cubical-term_wf face-type_wf cubical-type_wf context-subset_wf equal_wf face-and_wf subset-cubical-type face-term-implies-subset face-term-and-implies1 face-term-and-implies2 list_wf cubical_set_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation_alt introduction cut sqequalRule thin instantiate extract_by_obid sqequalHypSubstitution isectElimination productEquality cumulativity hypothesisEquality hypothesis lambdaEquality_alt spreadEquality applyEquality independent_isectElimination because_Cache inhabitedIsType productIsType universeIsType axiomEquality equalityTransitivity equalitySymmetry isect_memberEquality_alt isectIsTypeImplies

Latex:
\mforall{}[Gamma:j\mvdash{}].  \mforall{}[sys:(phi:\{Gamma  \mvdash{}  \_:\mBbbF{}\}  \mtimes{}  \{Gamma,  phi  \mvdash{}  \_\})  List].
    (compatible-system\{i:l\}(Gamma;sys)  \mmember{}  \mBbbP{}\{[i'  |  j']\})



Date html generated: 2020_05_20-PM-03_09_08
Last ObjectModification: 2020_04_06-PM-11_41_59

Theory : cubical!type!theory


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