Nuprl Lemma : name-morph-domain_subtype
∀[I,J:Cname List]. ∀[f:name-morph(I;J)]. name-morph-domain(f;I) ≡ {x:nameset(I)| ↑isname(f x)}
Proof
Definitions occuring in Statement :
name-morph-domain: name-morph-domain(f;I),
name-morph: name-morph(I;J),
isname: isname(z),
nameset: nameset(L),
coordinate_name: Cname,
list: T List,
assert: ↑b,
ext-eq: A ≡ B,
uall: ∀[x:A]. B[x],
set: {x:A| B[x]} ,
apply: f a
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
ext-eq: A ≡ B,
and: P ∧ Q,
subtype_rel: A ⊆r B,
name-morph: name-morph(I;J),
prop: ℙ,
name-morph-domain: name-morph-domain(f;I),
nameset: nameset(L),
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
implies: P ⇒ Q,
rev_implies: P ⇐ Q,
cand: A c∧ B
Lemmas referenced :
name-morph-domain_wf,
nameset_wf,
assert_wf,
isname_wf,
name-morph_wf,
list_wf,
coordinate_name_wf,
member_filter_2,
l_member_wf,
filter_wf5
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
independent_pairFormation,
lambdaEquality,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
setEquality,
applyEquality,
setElimination,
rename,
sqequalRule,
productElimination,
independent_pairEquality,
axiomEquality,
isect_memberEquality,
because_Cache,
dependent_functionElimination,
independent_functionElimination,
dependent_set_memberEquality
Latex:
\mforall{}[I,J:Cname List]. \mforall{}[f:name-morph(I;J)]. name-morph-domain(f;I) \mequiv{} \{x:nameset(I)| \muparrow{}isname(f x)\}
Date html generated:
2016_05_20-AM-09_30_26
Last ObjectModification:
2015_12_28-PM-04_47_06
Theory : cubical!sets
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