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: P ⇒ Q,
union: left + right
Definitions unfolded in proof :
uimplies: b supposing a,
guard: {T},
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
prop: ℙ,
true: True,
and: P ∧ Q,
euclidean-parallel-plane: EuclideanParPlane,
member: t ∈ T,
proj-point-sep: proj-point-sep(eu;p;q),
implies: P ⇒ 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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