Nuprl Lemma : name-comp-id-left
∀[I,J:Cname List]. ∀[f:name-morph(I;J)]. ((1 o f) = f ∈ name-morph(I;J))
Proof
Definitions occuring in Statement :
name-comp: (f o g),
id-morph: 1,
name-morph: name-morph(I;J),
coordinate_name: Cname,
list: T List,
uall: ∀[x:A]. B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
name-morph: name-morph(I;J),
so_lambda: λ2x.t[x],
implies: P ⇒ Q,
prop: ℙ,
so_apply: x[s],
all: ∀x:A. B[x],
id-morph: 1,
name-comp: (f o g),
uext: uext(g),
compose: f o g,
ifthenelse: if b then t else f fi ,
btrue: tt
Lemmas referenced :
all_wf,
nameset_wf,
assert_wf,
isname_wf,
equal_wf,
extd-nameset_wf,
name-morph_wf,
list_wf,
coordinate_name_wf,
isname-nameset
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
setElimination,
thin,
rename,
equalitySymmetry,
dependent_set_memberEquality,
hypothesis,
lemma_by_obid,
isectElimination,
hypothesisEquality,
sqequalRule,
lambdaEquality,
functionEquality,
applyEquality,
isect_memberEquality,
axiomEquality,
because_Cache,
functionExtensionality
Latex:
\mforall{}[I,J:Cname List]. \mforall{}[f:name-morph(I;J)]. ((1 o f) = f)
Date html generated:
2016_05_20-AM-09_31_48
Last ObjectModification:
2015_12_28-PM-04_45_45
Theory : cubical!sets
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