Nuprl Lemma : filling-structure_wf

[Gamma:j⊢]. ∀[A:{Gamma ⊢ _}].  (Gamma ⊢ Filling(A) ∈ 𝕌{[i' j'']})


Proof




Definitions occuring in Statement :  filling-structure: Gamma ⊢ Filling(A) cubical-type: {X ⊢ _} cubical_set: CubicalSet uall: [x:A]. B[x] member: t ∈ T universe: Type
Definitions unfolded in proof :  uall: [x:A]. B[x] member: t ∈ T filling-structure: Gamma ⊢ Filling(A) prop:
Lemmas referenced :  filling-function_wf uniform-filling-function_wf cubical-type_wf cubical_set_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation_alt introduction cut sqequalRule setEquality extract_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality hypothesis axiomEquality equalityTransitivity equalitySymmetry universeIsType isect_memberEquality_alt isectIsTypeImplies inhabitedIsType instantiate

Latex:
\mforall{}[Gamma:j\mvdash{}].  \mforall{}[A:\{Gamma  \mvdash{}  \_\}].    (Gamma  \mvdash{}  Filling(A)  \mmember{}  \mBbbU{}\{[i'  |  j'']\})



Date html generated: 2020_05_20-PM-04_41_39
Last ObjectModification: 2020_04_11-AM-11_16_36

Theory : cubical!type!theory


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