Nuprl Lemma : m-retraction-subtype1
∀[X,Y,A:Type]. ∀[d:metric(X)]. Retract(X ⟶ A) ⊆r Retract(Y ⟶ A) supposing A ⊆r Y supposing Y ⊆r X
Proof
Definitions occuring in Statement :
m-retraction: Retract(X ⟶ A),
metric: metric(X),
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,
subtype_rel: A ⊆r B,
member: t ∈ T,
m-retraction: Retract(X ⟶ A),
and: P ∧ Q,
so_lambda: λ2x.t[x],
so_apply: x[s],
all: ∀x:A. B[x],
cand: A c∧ B,
is-mfun: f:FUN(X;Y),
guard: {T},
prop: ℙ
Latex:
\mforall{}[X,Y,A:Type].
\mforall{}[d:metric(X)]. Retract(X {}\mrightarrow{} A) \msubseteq{}r Retract(Y {}\mrightarrow{} A) supposing A \msubseteq{}r Y supposing Y \msubseteq{}r X
Date html generated:
2020_05_20-AM-11_49_46
Last ObjectModification:
2019_11_18-PM-03_32_10
Theory : reals
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