Nuprl Lemma : csm-id_wf
∀[X:CubicalSet]. (1(X) ∈ X ⟶ X)
Proof
Definitions occuring in Statement :
csm-id: 1(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: 1(X),
cube-set-map: A ⟶ B,
ext-eq: A ≡ B,
and: P ∧ Q,
subtype_rel: A ⊆r B
Lemmas referenced :
cubical-set-is-functor,
identity-trans_wf,
name-cat_wf,
type-cat_wf,
cubical-set_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
productElimination,
thin,
instantiate,
isectElimination,
hypothesis,
hypothesisEquality,
applyEquality,
sqequalRule,
axiomEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[X:CubicalSet]. (1(X) \mmember{} X {}\mrightarrow{} X)
Date html generated:
2016_06_16-PM-05_36_02
Last ObjectModification:
2015_12_28-PM-04_37_45
Theory : cubical!sets
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