Nuprl Lemma : face-forall-map
∀[G,H:j⊢]. ∀[phi:{G ⊢ _:𝔽}]. ∀[s:H.𝕀 j⟶ G]. (s ∈ H, (∀ (phi)s).𝕀 j⟶ G, phi)
Proof
Definitions occuring in Statement :
face-forall: (∀ phi),
context-subset: Gamma, phi,
face-type: 𝔽,
interval-type: 𝕀,
cube-context-adjoin: X.A,
csm-ap-term: (t)s,
cubical-term: {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,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
and: P ∧ Q
Lemmas referenced :
cube-context-adjoin_wf,
interval-type_wf,
face-forall-type-subtype,
csm-ap-term_wf,
face-type_wf,
csm-face-type,
context-subset-map,
context-subset_wf,
face-forall_wf,
cube_set_map_subtype2,
sub_cubical_set_transitivity,
cc-fst_wf,
context-adjoin-subset2,
face-term-implies-subset,
face-forall-implies,
cube_set_map_wf,
cubical-term_wf,
cubical_set_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
cut,
thin,
instantiate,
introduction,
extract_by_obid,
hypothesis,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
sqequalRule,
Error :memTop,
equalityTransitivity,
equalitySymmetry,
applyEquality,
because_Cache,
independent_isectElimination,
independent_pairFormation,
universeIsType,
inhabitedIsType
Latex:
\mforall{}[G,H:j\mvdash{}]. \mforall{}[phi:\{G \mvdash{} \_:\mBbbF{}\}]. \mforall{}[s:H.\mBbbI{} j{}\mrightarrow{} G]. (s \mmember{} H, (\mforall{} (phi)s).\mBbbI{} j{}\mrightarrow{} G, phi)
Date html generated:
2020_05_20-PM-03_06_27
Last ObjectModification:
2020_04_06-PM-07_32_05
Theory : cubical!type!theory
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