Nuprl Lemma : prod-ss-point
∀[ss1,ss2:Top]. (Point(ss1 × ss2) ~ Point(ss1) × Point(ss2))
Proof
Definitions occuring in Statement :
prod-ss: ss1 × ss2,
ss-point: Point(ss),
uall: ∀[x:A]. B[x],
top: Top,
product: 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,
prod-ss: ss1 × ss2,
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{}[ss1,ss2:Top]. (Point(ss1 \mtimes{} ss2) \msim{} Point(ss1) \mtimes{} Point(ss2))
Date html generated:
2018_07_29-AM-10_11_07
Last ObjectModification:
2018_07_03-AM-10_33_39
Theory : constructive!algebra
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