Nuprl Lemma : iota-wf
∀[I:Cname List]. ∀[x:nameset(I)]. (iota(x) ∈ name-morph(I-[x];I))
Proof
Definitions occuring in Statement :
iota: iota(x),
name-morph: name-morph(I;J),
nameset: nameset(L),
cname_deq: CnameDeq,
coordinate_name: Cname,
list-diff: as-bs,
cons: [a / b],
nil: [],
list: T List,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
nameset: nameset(L),
subtype_rel: A ⊆r B,
uimplies: b supposing a,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
cand: A c∧ B
Lemmas referenced :
iota_wf,
list-diff_wf,
coordinate_name_wf,
cname_deq_wf,
cons_wf,
nil_wf,
nameset_wf,
list_wf,
nameset_subtype,
l_subset_cons,
list-diff-subset,
subtype_rel_self,
name-morph_subtype
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
setElimination,
thin,
rename,
lemma_by_obid,
isectElimination,
hypothesis,
hypothesisEquality,
applyEquality,
sqequalRule,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache,
independent_isectElimination,
dependent_functionElimination,
productElimination,
independent_functionElimination,
independent_pairFormation
Latex:
\mforall{}[I:Cname List]. \mforall{}[x:nameset(I)]. (iota(x) \mmember{} name-morph(I-[x];I))
Date html generated:
2016_05_20-AM-09_31_32
Last ObjectModification:
2015_12_28-PM-04_45_58
Theory : cubical!sets
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