Nuprl Definition : setimage
setimage{i:l}(x;b) ==
∃f:(z:coSet{i:l} × (z ∈ b)) ⟶ coSet{i:l}
((∀z1,z2:z:coSet{i:l} × (z ∈ b). (seteq(fst(z1);fst(z2)) ⇒ seteq(f z1;f z2)))
∧ (∀y:coSet{i:l}. ((y ∈ x) ⇐⇒ ∃z:z:coSet{i:l} × (z ∈ b). seteq(y;f z))))
Definitions occuring in Statement :
setmem: (x ∈ s),
seteq: seteq(s1;s2),
coSet: coSet{i:l},
pi1: fst(t),
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
iff: P ⇐⇒ Q,
implies: P ⇒ Q,
and: P ∧ Q,
apply: f a,
function: x:A ⟶ B[x],
product: x:A × B[x]
Definitions occuring in definition :
apply: f a,
seteq: seteq(s1;s2),
setmem: (x ∈ s),
coSet: coSet{i:l},
product: x:A × B[x],
exists: ∃x:A. B[x],
iff: P ⇐⇒ Q,
all: ∀x:A. B[x],
pi1: fst(t),
implies: P ⇒ Q,
and: P ∧ Q,
function: x:A ⟶ B[x]
FDL editor aliases :
setimage
Latex:
setimage\{i:l\}(x;b) ==
\mexists{}f:(z:coSet\{i:l\} \mtimes{} (z \mmember{} b)) {}\mrightarrow{} coSet\{i:l\}
((\mforall{}z1,z2:z:coSet\{i:l\} \mtimes{} (z \mmember{} b). (seteq(fst(z1);fst(z2)) {}\mRightarrow{} seteq(f z1;f z2)))
\mwedge{} (\mforall{}y:coSet\{i:l\}. ((y \mmember{} x) \mLeftarrow{}{}\mRightarrow{} \mexists{}z:z:coSet\{i:l\} \mtimes{} (z \mmember{} b). seteq(y;f z))))
Date html generated:
2018_07_29-AM-10_08_33
Last ObjectModification:
2018_07_18-PM-09_09_36
Theory : constructive!set!theory
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