Nuprl Lemma : subset_iota_wf
∀[I:fset(ℕ)]. ∀[psi:𝔽(I)]. (subset_iota(psi) ∈ I,psi ⟶ formal-cube(I))
Proof
Definitions occuring in Statement :
subset_iota: subset_iota(psi),
cubical-subset: I,psi,
face-presheaf: 𝔽,
cube_set_map: A ⟶ B,
formal-cube: formal-cube(I),
I_cube: A(I),
fset: fset(T),
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
subset_iota: subset_iota(psi),
subset-iota: iota,
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B
Lemmas referenced :
face-presheaf_wf,
subset-iota_wf,
I_cube_wf,
small_cubical_set_subtype,
fset_wf,
nat_wf
Rules used in proof :
cut,
instantiate,
introduction,
extract_by_obid,
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation_alt,
thin,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
universeIsType,
applyEquality,
isect_memberEquality_alt,
isectIsTypeImplies,
inhabitedIsType
Latex:
\mforall{}[I:fset(\mBbbN{})]. \mforall{}[psi:\mBbbF{}(I)]. (subset\_iota(psi) \mmember{} I,psi {}\mrightarrow{} formal-cube(I))
Date html generated:
2020_05_20-PM-01_45_34
Last ObjectModification:
2020_04_03-PM-04_25_37
Theory : cubical!type!theory
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