Nuprl Lemma : csm-ap-id-term
∀[Gamma:CubicalSet]. ∀[A:{Gamma ⊢ _}]. ∀[t:{Gamma ⊢ _:A}]. ((t)1(Gamma) = t ∈ {Gamma ⊢ _:A})
Proof
Definitions occuring in Statement :
csm-ap-term: (t)s,
cubical-term: {X ⊢ _:AF},
cubical-type: {X ⊢ _},
csm-id: 1(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,
cubical-term: {X ⊢ _:AF},
csm-id: 1(X),
csm-ap-term: (t)s,
type-cat: TypeCat,
identity-trans: identity-trans(C;D;F),
csm-ap: (s)x,
cat-id: cat-id(C),
pi2: snd(t),
pi1: fst(t),
so_lambda: λ2x.t[x],
cubical-type: {X ⊢ _},
so_apply: x[s],
all: ∀x:A. B[x],
prop: ℙ
Lemmas referenced :
cubical-term_wf,
cubical-type_wf,
cubical-set_wf,
I-cube_wf,
list_wf,
coordinate_name_wf,
all_wf,
name-morph_wf,
equal_wf,
cube-set-restriction_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
equalitySymmetry,
sqequalHypSubstitution,
setElimination,
thin,
rename,
dependent_set_memberEquality,
hypothesis,
lemma_by_obid,
isectElimination,
hypothesisEquality,
sqequalRule,
isect_memberEquality,
axiomEquality,
because_Cache,
functionExtensionality,
applyEquality,
lambdaEquality,
productElimination
Latex:
\mforall{}[Gamma:CubicalSet]. \mforall{}[A:\{Gamma \mvdash{} \_\}]. \mforall{}[t:\{Gamma \mvdash{} \_:A\}]. ((t)1(Gamma) = t)
Date html generated:
2016_06_16-PM-05_40_30
Last ObjectModification:
2015_12_28-PM-04_35_26
Theory : cubical!sets
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