Nuprl Lemma : prod-ss-sep
∀[ss1,ss2,x,y:Top]. (x # y ~ fst(x) # fst(y) ∨ snd(x) # snd(y))
Proof
Definitions occuring in Statement :
prod-ss: ss1 × ss2,
ss-sep: x # y,
uall: ∀[x:A]. B[x],
top: Top,
pi1: fst(t),
pi2: snd(t),
or: P ∨ Q,
sqequal: s ~ t
Definitions unfolded in proof :
or: P ∨ Q,
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-sep: x # y,
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,x,y:Top]. (x \# y \msim{} fst(x) \# fst(y) \mvee{} snd(x) \# snd(y))
Date html generated:
2018_07_29-AM-10_11_09
Last ObjectModification:
2018_07_03-AM-10_35_27
Theory : constructive!algebra
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