Nuprl Lemma : ss-fun-point
∀[X,Y:Top]. (Point(X ⟶ Y) ~ {f:Point(X) ⟶ Point(Y)| ss-function(X;Y;f)} )
Proof
Definitions occuring in Statement :
ss-fun: X ⟶ Y,
ss-function: ss-function(X;Y;f),
ss-point: Point(ss),
uall: ∀[x:A]. B[x],
top: Top,
set: {x:A| B[x]} ,
function: x:A ⟶ B[x],
sqequal: s ~ t
Definitions unfolded in proof :
all: ∀x:A. B[x],
ss-function: ss-function(X;Y;f),
fun-ss: A ⟶ ss,
btrue: tt,
bfalse: ff,
eq_atom: x =a y,
ifthenelse: if b then t else f fi ,
record-update: r[x := v],
mk-ss: Point=P #=Sep symm=Sym cotrans=C,
set-ss: {x:ss | P[x]},
ss-fun: X ⟶ Y,
record-select: r.x,
ss-point: Point(ss),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
top_wf
Rules used in proof :
because_Cache,
hypothesisEquality,
thin,
isectElimination,
isect_memberEquality,
sqequalHypSubstitution,
extract_by_obid,
sqequalAxiom,
hypothesis,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[X,Y:Top]. (Point(X {}\mrightarrow{} Y) \msim{} \{f:Point(X) {}\mrightarrow{} Point(Y)| ss-function(X;Y;f)\} )
Date html generated:
2018_07_29-AM-10_11_39
Last ObjectModification:
2018_07_04-AM-11_56_59
Theory : constructive!algebra
Home
Index