Nuprl Lemma : fixedpoint-property_functionality
∀X:Type. ∀d:metric(X). ∀Y:Type. ∀d':metric(Y). (homeomorphic(X;d;Y;d') ⇒ mcompact(X;d) ⇒ FP(X) ⇒ FP(Y))
Proof
Definitions occuring in Statement :
mcompact: mcompact(X;d),
fixedpoint-property: FP(X),
homeomorphic: homeomorphic(X;dX;Y;dY),
metric: metric(X),
all: ∀x:A. B[x],
implies: P ⇒ Q,
universe: Type
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
homeomorphic: homeomorphic(X;dX;Y;dY),
exists: ∃x:A. B[x],
sq_exists: ∃x:A [B[x]],
member: t ∈ T,
fixedpoint-property: FP(X),
m-unif-cont: UC(f:X ⟶ Y),
uall: ∀[x:A]. B[x],
mfun: FUN(X ⟶ Y),
and: P ∧ Q,
nat_plus: ℕ+,
uimplies: b supposing a,
rneq: x ≠ y,
guard: {T},
or: P ∨ Q,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
rless: x < y,
decidable: Dec(P),
not: ¬A,
satisfiable_int_formula: satisfiable_int_formula(fmla),
false: False,
top: Top,
prop: ℙ,
subtype_rel: A ⊆r B,
mcompose: mcompose(f;g),
compose: f o g,
sq_stable: SqStable(P),
squash: ↓T,
uiff: uiff(P;Q)
Latex:
\mforall{}X:Type. \mforall{}d:metric(X). \mforall{}Y:Type. \mforall{}d':metric(Y).
(homeomorphic(X;d;Y;d') {}\mRightarrow{} mcompact(X;d) {}\mRightarrow{} FP(X) {}\mRightarrow{} FP(Y))
Date html generated:
2020_05_20-PM-00_00_08
Last ObjectModification:
2019_11_20-PM-02_31_10
Theory : reals
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