Nuprl Lemma : ss-sep-or

ss:SeparationSpace. ∀x,y,z:Point.  (x  (x z ∨ z))


Proof




Definitions occuring in Statement :  ss-sep: y ss-point: Point separation-space: SeparationSpace all: x:A. B[x] implies:  Q or: P ∨ Q
Definitions unfolded in proof :  or: P ∨ Q implies:  Q so_apply: x[s] so_lambda: λ2x.t[x] prop: guard: {T} uall: [x:A]. B[x] btrue: tt ifthenelse: if then else fi  eq_atom: =a y subtype_rel: A ⊆B record-select: r.x record+: record+ separation-space: SeparationSpace ss-point: Point ss-sep: 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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