Nuprl Lemma : name-morph_subtype_domain
∀[I,J:Cname List]. ∀[f:name-morph(I;J)]. (f ∈ name-morph-domain(f;I) ⟶ nameset(J))
Proof
Definitions occuring in Statement :
name-morph-domain: name-morph-domain(f;I),
name-morph: name-morph(I;J),
nameset: nameset(L),
coordinate_name: Cname,
list: T List,
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ⟶ B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
name-morph: name-morph(I;J),
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a,
all: ∀x:A. B[x],
top: Top,
name-morph-domain: name-morph-domain(f;I),
nameset: nameset(L),
prop: ℙ,
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
uiff: uiff(P;Q)
Lemmas referenced :
subtype_rel_dep_function,
nameset_wf,
extd-nameset_wf,
top_wf,
member_filter_2,
coordinate_name_wf,
isname_wf,
l_member_wf,
name-morph-domain_wf,
all_wf,
assert_wf,
equal_wf,
name-morph_wf,
list_wf,
assert-isname
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
cut,
sqequalHypSubstitution,
setElimination,
thin,
rename,
hypothesisEquality,
applyEquality,
lemma_by_obid,
isectElimination,
hypothesis,
sqequalRule,
lambdaEquality,
voidEquality,
independent_isectElimination,
voidElimination,
lambdaFormation,
isect_memberEquality,
because_Cache,
functionExtensionality,
dependent_functionElimination,
setEquality,
productElimination,
independent_functionElimination,
dependent_set_memberEquality,
functionEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[I,J:Cname List]. \mforall{}[f:name-morph(I;J)]. (f \mmember{} name-morph-domain(f;I) {}\mrightarrow{} nameset(J))
Date html generated:
2016_05_20-AM-09_30_34
Last ObjectModification:
2015_12_28-PM-04_46_45
Theory : cubical!sets
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