Nuprl Lemma : context-map_wf_cubical-subset
∀[Gamma:j⊢]. ∀[I:fset(ℕ)]. ∀[rho:Gamma(I)]. ∀[psi:𝔽(I)]. (<rho> ∈ I,psi j⟶ Gamma)
Proof
Definitions occuring in Statement :
cubical-subset: I,psi,
face-presheaf: 𝔽,
context-map: <rho>,
cube_set_map: A ⟶ B,
I_cube: A(I),
cubical_set: CubicalSet,
fset: fset(T),
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
subtype_rel: A ⊆r B
Lemmas referenced :
context-map_wf,
csm-subtype-cubical-subset,
I_cube_wf,
face-presheaf_wf2,
fset_wf,
nat_wf,
cubical_set_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
hypothesis,
applyEquality,
instantiate,
isectElimination,
sqequalRule,
universeIsType
Latex:
\mforall{}[Gamma:j\mvdash{}]. \mforall{}[I:fset(\mBbbN{})]. \mforall{}[rho:Gamma(I)]. \mforall{}[psi:\mBbbF{}(I)]. (<rho> \mmember{} I,psi j{}\mrightarrow{} Gamma)
Date html generated:
2020_05_20-PM-04_20_23
Last ObjectModification:
2020_04_10-AM-05_47_13
Theory : cubical!type!theory
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