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 :
all: ∀x:A. B[x],
member: t ∈ T,
ss-sep: x # y,
ss-point: Point,
separation-space: SeparationSpace,
record+: record+,
record-select: r.x,
subtype_rel: A ⊆r B,
eq_atom: x =a y,
ifthenelse: if b then t else f fi ,
btrue: tt,
uall: ∀[x:A]. B[x],
guard: {T},
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
implies: P ⇒ Q,
or: P ∨ Q
Lemmas referenced :
subtype_rel_self,
all_wf,
not_wf,
or_wf,
separation-space_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
introduction,
sqequalRule,
sqequalHypSubstitution,
dependentIntersectionElimination,
dependentIntersectionEqElimination,
thin,
cut,
hypothesis,
applyEquality,
tokenEquality,
instantiate,
extract_by_obid,
isectElimination,
universeEquality,
setEquality,
functionEquality,
equalityTransitivity,
equalitySymmetry,
lambdaEquality,
cumulativity,
hypothesisEquality,
because_Cache,
functionExtensionality,
setElimination,
rename
Latex:
\mforall{}ss:SeparationSpace. \mforall{}x,y,z:Point. (x \# y {}\mRightarrow{} (x \# z \mvee{} y \# z))
Date html generated:
2017_10_02-PM-03_24_06
Last ObjectModification:
2017_06_22-PM-06_55_26
Theory : constructive!algebra
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