Nuprl Lemma : prod-ss_wf
∀[ss1,ss2:SeparationSpace]. (ss1 × ss2 ∈ SeparationSpace)
Proof
Definitions occuring in Statement :
prod-ss: ss1 × ss2,
separation-space: SeparationSpace,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
pi2: snd(t),
pi1: fst(t),
false: False,
not: ¬A,
top: Top,
prod-ss: ss1 × ss2,
ss-point: Point,
ss-sep: x # y,
or: P ∨ Q,
all: ∀x:A. B[x],
implies: P ⇒ Q,
so_apply: x[s],
so_lambda: λ2x.t[x],
prop: ℙ,
guard: {T},
btrue: tt,
ifthenelse: if b then t else f fi ,
eq_atom: x =a y,
subtype_rel: A ⊆r B,
record-select: r.x,
record+: record+,
separation-space: SeparationSpace,
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
separation-space_wf,
equal_wf,
ss-sep-irrefl,
pi2_wf,
pi1_wf_top,
ss-sep_wf,
mk-ss_wf,
or_wf,
not_wf,
all_wf,
subtype_rel_self
Rules used in proof :
axiomEquality,
dependent_functionElimination,
inrEquality,
inlEquality,
independent_functionElimination,
unionElimination,
lambdaFormation,
voidEquality,
voidElimination,
isect_memberEquality,
independent_pairEquality,
productElimination,
dependent_set_memberEquality,
productEquality,
rename,
setElimination,
functionExtensionality,
because_Cache,
cumulativity,
lambdaEquality,
equalitySymmetry,
equalityTransitivity,
functionEquality,
setEquality,
universeEquality,
isectElimination,
extract_by_obid,
instantiate,
tokenEquality,
applyEquality,
hypothesis,
thin,
dependentIntersectionEqElimination,
sqequalRule,
dependentIntersectionElimination,
sqequalHypSubstitution,
hypothesisEquality,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[ss1,ss2:SeparationSpace]. (ss1 \mtimes{} ss2 \mmember{} SeparationSpace)
Date html generated:
2016_11_08-AM-09_12_01
Last ObjectModification:
2016_11_02-AM-11_39_06
Theory : inner!product!spaces
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