Nuprl Lemma : m-retraction_functionality
∀[X,Y:Type].
∀[A,B:Type]. ∀[d:metric(X)]. Retract(X ⟶ A) ≡ Retract(Y ⟶ B) supposing A ⊆r X supposing A ≡ B supposing X ≡ Y
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],
uimplies: b supposing a,
ext-eq: A ≡ B,
and: P ∧ Q,
subtype_rel: A ⊆r B,
member: t ∈ T,
m-retraction: Retract(X ⟶ A),
so_lambda: λ2x.t[x],
so_apply: x[s],
guard: {T},
all: ∀x:A. B[x],
cand: A c∧ B,
is-mfun: f:FUN(X;Y),
prop: ℙ
Latex:
\mforall{}[X,Y:Type].
\mforall{}[A,B:Type]. \mforall{}[d:metric(X)]. Retract(X {}\mrightarrow{} A) \mequiv{} Retract(Y {}\mrightarrow{} B) supposing A \msubseteq{}r X supposing A \mequiv{} B
supposing X \mequiv{} Y
Date html generated:
2020_05_20-AM-11_49_26
Last ObjectModification:
2019_11_20-PM-11_42_13
Theory : reals
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