Nuprl Lemma : proj-point-sep-symmetry

e:EuclideanParPlane. ∀x,y:Point Line.  (proj-point-sep(e;x;y)  proj-point-sep(e;y;x))


Proof




Definitions occuring in Statement :  proj-point-sep: proj-point-sep(eu;p;q) euclidean-parallel-plane: EuclideanParPlane geo-line: Line geo-point: Point all: x:A. B[x] implies:  Q union: left right
Definitions unfolded in proof :  uimplies: supposing a guard: {T} subtype_rel: A ⊆B uall: [x:A]. B[x] prop: true: True and: P ∧ Q euclidean-parallel-plane: EuclideanParPlane member: t ∈ T proj-point-sep: proj-point-sep(eu;p;q) implies:  Q all: x:A. B[x]
Lemmas referenced :  geo-line_wf geo-primitives_wf euclidean-plane-structure_wf euclidean-plane_wf euclidean-parallel-plane_wf subtype_rel_transitivity euclidean-planes-subtype euclidean-plane-subtype euclidean-plane-structure-subtype geo-point_wf proj-point-sep_wf geo-intersect-symmetry euclidean-plane-axioms
Rules used in proof :  sqequalRule independent_isectElimination instantiate applyEquality unionEquality isectElimination because_Cache natural_numberEquality independent_functionElimination productElimination hypothesis hypothesisEquality rename setElimination dependent_functionElimination extract_by_obid introduction cut sqequalHypSubstitution thin unionElimination lambdaFormation sqequalReflexivity computationStep sqequalTransitivity sqequalSubstitution

Latex:
\mforall{}e:EuclideanParPlane.  \mforall{}x,y:Point  +  Line.    (proj-point-sep(e;x;y)  {}\mRightarrow{}  proj-point-sep(e;y;x))



Date html generated: 2018_05_22-PM-01_13_52
Last ObjectModification: 2018_05_21-PM-02_21_22

Theory : euclidean!plane!geometry


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