Nuprl Lemma : csm-id-comp
∀[A,B:j⊢]. ∀[sigma:A j⟶ B]. ((sigma o 1(A) = sigma ∈ A j⟶ B) ∧ (1(B) o sigma = sigma ∈ A j⟶ B))
Proof
Definitions occuring in Statement :
csm-id: 1(X),
csm-comp: G o F,
cube_set_map: A ⟶ B,
cubical_set: CubicalSet,
uall: ∀[x:A]. B[x],
and: P ∧ Q,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
cubical_set: CubicalSet,
cube_set_map: A ⟶ B,
csm-comp: G o F,
pscm-comp: G o F,
csm-id: 1(X),
pscm-id: 1(X)
Lemmas referenced :
pscm-id-comp,
cube-cat_wf
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isectElimination,
thin,
hypothesis,
sqequalRule
Latex:
\mforall{}[A,B:j\mvdash{}]. \mforall{}[sigma:A j{}\mrightarrow{} B]. ((sigma o 1(A) = sigma) \mwedge{} (1(B) o sigma = sigma))
Date html generated:
2020_05_20-PM-01_42_02
Last ObjectModification:
2020_04_03-PM-03_34_05
Theory : cubical!type!theory
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