Nuprl Lemma : cc-fst_wf
∀[Gamma:CubicalSet]. ∀[A:{Gamma ⊢ _}]. (p ∈ Gamma.A ⟶ Gamma)
Proof
Definitions occuring in Statement :
cc-fst: p,
cube-context-adjoin: X.A,
cubical-type: {X ⊢ _},
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,
cc-fst: p,
all: ∀x:A. B[x],
so_lambda: λ2x.t[x],
so_apply: x[s],
prop: ℙ,
cube-context-adjoin: X.A,
I-cube: X(I),
top: Top,
functor-ob: ob(F),
cube-set-restriction: f(s),
pi2: snd(t),
pi1: fst(t),
implies: P ⇒ Q
Lemmas referenced :
cube-set-map-is,
cube-context-adjoin_wf,
pi1_wf_top,
I-cube_wf,
list_wf,
coordinate_name_wf,
name-morph_wf,
all_wf,
equal_wf,
cube-set-restriction_wf,
cubical-type_wf,
cubical-set_wf,
ob_pair_lemma
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
dependent_set_memberEquality,
lambdaEquality,
lambdaFormation,
because_Cache,
functionEquality,
applyEquality,
functionExtensionality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
dependent_functionElimination,
voidElimination,
voidEquality,
productElimination,
independent_pairEquality,
independent_functionElimination
Latex:
\mforall{}[Gamma:CubicalSet]. \mforall{}[A:\{Gamma \mvdash{} \_\}]. (p \mmember{} Gamma.A {}\mrightarrow{} Gamma)
Date html generated:
2017_10_05-AM-10_13_26
Last ObjectModification:
2017_07_28-AM-11_18_53
Theory : cubical!sets
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