Nuprl Lemma : cc-fst+-1-type
∀[G:j⊢]. ∀[A:{G.𝕀 ⊢ _}]. (((A)[1(𝕀)])p = ((A)p+)[1(𝕀)] ∈ {G.𝕀 ⊢ _})
Proof
Definitions occuring in Statement :
interval-1: 1(𝕀),
interval-type: 𝕀,
csm+: tau+,
csm-id-adjoin: [u],
cc-fst: p,
cube-context-adjoin: X.A,
csm-ap-type: (AF)s,
cubical-type: {X ⊢ _},
cubical_set: CubicalSet,
uall: ∀[x:A]. B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
true: True,
squash: ↓T,
prop: ℙ
Lemmas referenced :
cubical-type_wf,
cube-context-adjoin_wf,
cubical_set_cumulativity-i-j,
interval-type_wf,
cubical_set_wf,
csm-id-adjoin_wf-interval-1,
cc-fst_wf,
csm-comp-type,
cc-fst+-comp-1,
csm-ap-type_wf,
squash_wf,
true_wf,
cube_set_map_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
universeIsType,
cut,
thin,
instantiate,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
applyEquality,
hypothesis,
sqequalRule,
Error :memTop,
equalitySymmetry,
natural_numberEquality,
lambdaEquality_alt,
imageElimination,
equalityTransitivity,
inhabitedIsType,
imageMemberEquality,
baseClosed
Latex:
\mforall{}[G:j\mvdash{}]. \mforall{}[A:\{G.\mBbbI{} \mvdash{} \_\}]. (((A)[1(\mBbbI{})])p = ((A)p+)[1(\mBbbI{})])
Date html generated:
2020_05_20-PM-04_44_04
Last ObjectModification:
2020_04_10-AM-11_26_14
Theory : cubical!type!theory
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