Nuprl Lemma : member-poset-cat-arrow
∀[I:Cname List]. ∀[x,y:cat-ob(poset-cat(I))]. λx.Ax ∈ cat-arrow(poset-cat(I)) x y supposing cat-arrow(poset-cat(I)) x y
Proof
Definitions occuring in Statement :
poset-cat: poset-cat(J),
coordinate_name: Cname,
cat-arrow: cat-arrow(C),
cat-ob: cat-ob(C),
list: T List,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
member: t ∈ T,
apply: f a,
lambda: λx.A[x],
axiom: Ax
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a
Lemmas referenced :
poset-cat-arrow-equals,
cat-arrow_wf,
poset-cat_wf,
cat-ob_wf,
list_wf,
coordinate_name_wf
Rules used in proof :
cut,
lemma_by_obid,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
introduction,
rename,
equalityTransitivity,
equalitySymmetry,
sqequalRule,
axiomEquality,
applyEquality
Latex:
\mforall{}[I:Cname List]. \mforall{}[x,y:cat-ob(poset-cat(I))].
\mlambda{}x.Ax \mmember{} cat-arrow(poset-cat(I)) x y supposing cat-arrow(poset-cat(I)) x y
Date html generated:
2016_06_16-PM-06_52_47
Last ObjectModification:
2015_12_28-PM-04_22_32
Theory : cubical!sets
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