Nuprl Lemma : face-map_wf_fresh-cname
∀[L:Cname List]. ∀[p:ℕ2]. ((fresh-cname(L):=p) ∈ name-morph(L+;L))
Proof
Definitions occuring in Statement :
face-map: (x:=i),
name-morph: name-morph(I;J),
add-fresh-cname: I+,
fresh-cname: fresh-cname(I),
coordinate_name: Cname,
list: T List,
int_seg: {i..j-},
uall: ∀[x:A]. B[x],
member: t ∈ T,
natural_number: $n
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
add-fresh-cname: I+,
has-value: (a)↓,
prop: ℙ,
uimplies: b supposing a,
so_lambda: λ2x.t[x],
so_apply: x[s],
subtype_rel: A ⊆r B
Lemmas referenced :
value-type-has-value,
coordinate_name_wf,
not_wf,
l_member_wf,
set-value-type,
coordinate_name-value-type,
fresh-cname_wf,
face-map_wf,
int_seg_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
callbyvalueReduce,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
setEquality,
hypothesis,
hypothesisEquality,
independent_isectElimination,
lambdaEquality,
applyEquality,
setElimination,
rename,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
natural_numberEquality,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[L:Cname List]. \mforall{}[p:\mBbbN{}2]. ((fresh-cname(L):=p) \mmember{} name-morph(L+;L))
Date html generated:
2016_05_20-AM-09_31_38
Last ObjectModification:
2015_12_28-PM-04_45_53
Theory : cubical!sets
Home
Index