Nuprl Lemma : fun-ss-point
∀[ss,A:Top]. (Point(A ⟶ ss) ~ A ⟶ Point(ss))
Proof
Definitions occuring in Statement :
fun-ss: A ⟶ ss,
ss-point: Point(ss),
uall: ∀[x:A]. B[x],
top: Top,
function: x:A ⟶ B[x],
sqequal: s ~ t
Definitions unfolded in proof :
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,
fun-ss: A ⟶ ss,
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{}[ss,A:Top]. (Point(A {}\mrightarrow{} ss) \msim{} A {}\mrightarrow{} Point(ss))
Date html generated:
2018_07_29-AM-10_11_00
Last ObjectModification:
2018_07_03-PM-01_02_45
Theory : constructive!algebra
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