Nuprl Lemma : csm-id-adjoin_wf
∀[Gamma:CubicalSet]. ∀[A:{Gamma ⊢ _}]. ∀[u:{Gamma ⊢ _:A}]. ([u] ∈ Gamma ⟶ Gamma.A)
Proof
Definitions occuring in Statement :
csm-id-adjoin: [u],
cube-context-adjoin: X.A,
cubical-term: {X ⊢ _:AF},
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,
csm-id-adjoin: [u],
subtype_rel: A ⊆r B,
uimplies: b supposing a,
squash: ↓T,
prop: ℙ,
true: True,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q
Lemmas referenced :
csm-adjoin_wf,
csm-id_wf,
subtype_rel-equal,
cubical-term_wf,
csm-ap-type_wf,
equal_wf,
squash_wf,
true_wf,
csm-ap-id-type,
iff_weakening_equal,
cubical-type_wf,
cubical-set_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
because_Cache,
hypothesis,
applyEquality,
independent_isectElimination,
instantiate,
lambdaEquality,
imageElimination,
equalityTransitivity,
equalitySymmetry,
universeEquality,
natural_numberEquality,
imageMemberEquality,
baseClosed,
productElimination,
independent_functionElimination,
axiomEquality,
isect_memberEquality
Latex:
\mforall{}[Gamma:CubicalSet]. \mforall{}[A:\{Gamma \mvdash{} \_\}]. \mforall{}[u:\{Gamma \mvdash{} \_:A\}]. ([u] \mmember{} Gamma {}\mrightarrow{} Gamma.A)
Date html generated:
2017_10_05-AM-10_13_34
Last ObjectModification:
2017_07_28-AM-11_18_59
Theory : cubical!sets
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