Nuprl Lemma : m-retraction-subtype2
∀[X,A,B:Type]. ∀[d:metric(X)]. Retract(X ⟶ A) ⊆r Retract(X ⟶ B) supposing B ⊆r X supposing A ≡ B
Proof
Definitions occuring in Statement :
m-retraction: Retract(X ⟶ A),
metric: metric(X),
ext-eq: A ≡ B,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
prop: ℙ,
ext-eq: A ≡ B,
and: P ∧ Q,
guard: {T}
Latex:
\mforall{}[X,A,B:Type]. \mforall{}[d:metric(X)]. Retract(X {}\mrightarrow{} A) \msubseteq{}r Retract(X {}\mrightarrow{} B) supposing B \msubseteq{}r X supposing A \mequiv{} B
Date html generated:
2020_05_20-AM-11_50_06
Last ObjectModification:
2019_11_20-PM-11_45_03
Theory : reals
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