Nuprl Lemma : csm-id-adjoin-ap
∀X:CubicalSet. ∀A:{X ⊢ _}. ∀u:{X ⊢ _:A}. ∀I:Cname List. ∀a:X(I). (([u])a = (a;u I a) ∈ X.A(I))
Proof
Definitions occuring in Statement :
csm-id-adjoin: [u],
cc-adjoin-cube: (v;u),
cube-context-adjoin: X.A,
cubical-term: {X ⊢ _:AF},
cubical-type: {X ⊢ _},
csm-ap: (s)x,
I-cube: X(I),
cubical-set: CubicalSet,
coordinate_name: Cname,
list: T List,
all: ∀x:A. B[x],
apply: f a,
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
cubical-term: {X ⊢ _:AF},
csm-id-adjoin: [u],
csm-ap: (s)x,
csm-id: 1(X),
csm-adjoin: (s;u),
identity-trans: identity-trans(C;D;F),
cat-id: cat-id(C),
type-cat: TypeCat,
pi2: snd(t),
pi1: fst(t),
cc-adjoin-cube: (v;u),
member: t ∈ T,
cubical-type-at: A(a),
uall: ∀[x:A]. B[x]
Lemmas referenced :
cc-adjoin-cube_wf,
I-cube_wf,
list_wf,
coordinate_name_wf,
cubical-term_wf,
cubical-type_wf,
cubical-set_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
sqequalHypSubstitution,
setElimination,
thin,
rename,
sqequalRule,
lemma_by_obid,
dependent_functionElimination,
hypothesisEquality,
applyEquality,
hypothesis,
isectElimination
Latex:
\mforall{}X:CubicalSet. \mforall{}A:\{X \mvdash{} \_\}. \mforall{}u:\{X \mvdash{} \_:A\}. \mforall{}I:Cname List. \mforall{}a:X(I). (([u])a = (a;u I a))
Date html generated:
2016_06_16-PM-05_41_44
Last ObjectModification:
2015_12_28-PM-04_34_20
Theory : cubical!sets
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