Nuprl Lemma : iota'-identity
∀[I:Cname List]. ∀[i:ℕ2]. ((iota'(I) o (fresh-cname(I):=i)) = 1 ∈ name-morph(I;I))
Proof
Definitions occuring in Statement :
name-comp: (f o g),
iota': iota'(I),
face-map: (x:=i),
id-morph: 1,
name-morph: name-morph(I;J),
fresh-cname: fresh-cname(I),
coordinate_name: Cname,
list: T List,
int_seg: {i..j-},
uall: ∀[x:A]. B[x],
natural_number: $n,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
iota': iota'(I),
subtype_rel: A ⊆r B,
prop: ℙ,
uimplies: b supposing a,
all: ∀x:A. B[x]
Lemmas referenced :
iota-identity,
fresh-cname_wf,
coordinate_name_wf,
not_wf,
l_member_wf,
fresh-cname-not-member2,
int_seg_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
applyEquality,
lambdaEquality,
setElimination,
rename,
setEquality,
sqequalRule,
independent_isectElimination,
dependent_functionElimination,
natural_numberEquality,
isect_memberEquality,
axiomEquality,
because_Cache
Latex:
\mforall{}[I:Cname List]. \mforall{}[i:\mBbbN{}2]. ((iota'(I) o (fresh-cname(I):=i)) = 1)
Date html generated:
2016_05_20-AM-09_33_34
Last ObjectModification:
2015_12_28-PM-04_44_53
Theory : cubical!sets
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