Nuprl Lemma : name-morph-range_wf
∀[I,J:Cname List]. ∀[f:name-morph(I;J)]. (name-morph-range(f;I) ∈ Type)
Proof
Definitions occuring in Statement :
name-morph-range: name-morph-range(f;I),
name-morph: name-morph(I;J),
coordinate_name: Cname,
list: T List,
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
name-morph-range: name-morph-range(f;I),
so_lambda: λ2x.t[x],
prop: ℙ,
and: P ∧ Q,
name-morph: name-morph(I;J),
uiff: uiff(P;Q),
uimplies: b supposing a,
subtype_rel: A ⊆r B,
guard: {T},
nameset: nameset(L),
so_apply: x[s],
exists: ∃x:A. B[x]
Lemmas referenced :
coordinate_name_wf,
exists_wf,
nameset_wf,
assert_wf,
isname_wf,
equal_wf,
assert-isname,
name-morph_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
setEquality,
extract_by_obid,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
sqequalRule,
lambdaEquality,
productEquality,
applyEquality,
setElimination,
rename,
because_Cache,
productElimination,
independent_isectElimination,
equalityTransitivity,
equalitySymmetry,
axiomEquality,
isect_memberEquality
Latex:
\mforall{}[I,J:Cname List]. \mforall{}[f:name-morph(I;J)]. (name-morph-range(f;I) \mmember{} Type)
Date html generated:
2017_10_05-AM-10_05_59
Last ObjectModification:
2017_07_28-AM-11_16_12
Theory : cubical!sets
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