Nuprl Lemma : swap-intervals_wf
∀[Gamma:j⊢]. (swap-intervals(Gamma) ∈ Gamma.𝕀.𝕀 j⟶ Gamma.𝕀.𝕀)
Proof
Definitions occuring in Statement :
swap-intervals: swap-intervals(G),
interval-type: 𝕀,
cube-context-adjoin: X.A,
cube_set_map: A ⟶ B,
cubical_set: CubicalSet,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
swap-intervals: swap-intervals(G)
Lemmas referenced :
cubical_set_wf,
interval-type_wf,
csm-swap_wf,
csm-interval-type
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
sqequalHypSubstitution,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
universeIsType,
instantiate,
extract_by_obid,
hypothesisEquality,
thin,
isectElimination,
Error :memTop
Latex:
\mforall{}[Gamma:j\mvdash{}]. (swap-intervals(Gamma) \mmember{} Gamma.\mBbbI{}.\mBbbI{} j{}\mrightarrow{} Gamma.\mBbbI{}.\mBbbI{})
Date html generated:
2020_05_20-PM-02_40_10
Last ObjectModification:
2020_04_04-PM-02_52_51
Theory : cubical!type!theory
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