Nuprl Lemma : ss-sep-or
∀ss:SeparationSpace. ∀x,y,z:Point. (x # y ⇒ (x # z ∨ y # z))
Proof
Definitions occuring in Statement :
ss-sep: x # y,
ss-point: Point,
separation-space: SeparationSpace,
all: ∀x:A. B[x],
implies: P ⇒ Q,
or: P ∨ Q
Definitions unfolded in proof :
or: P ∨ Q,
implies: P ⇒ Q,
so_apply: x[s],
so_lambda: λ2x.t[x],
prop: ℙ,
guard: {T},
uall: ∀[x:A]. B[x],
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,
ss-point: Point,
ss-sep: x # y,
member: t ∈ T,
all: ∀x:A. B[x]
Lemmas referenced :
separation-space_wf,
or_wf,
not_wf,
all_wf,
subtype_rel_self
Rules used in proof :
rename,
setElimination,
functionExtensionality,
because_Cache,
hypothesisEquality,
cumulativity,
lambdaEquality,
equalitySymmetry,
equalityTransitivity,
functionEquality,
setEquality,
universeEquality,
isectElimination,
extract_by_obid,
instantiate,
tokenEquality,
applyEquality,
hypothesis,
cut,
thin,
dependentIntersectionEqElimination,
dependentIntersectionElimination,
sqequalHypSubstitution,
sqequalRule,
introduction,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}ss:SeparationSpace. \mforall{}x,y,z:Point. (x \# y {}\mRightarrow{} (x \# z \mvee{} y \# z))
Date html generated:
2016_11_08-AM-09_10_52
Last ObjectModification:
2016_11_02-PM-03_16_07
Theory : inner!product!spaces
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