Nuprl Lemma : geo-perp-symmetry2
∀e:BasicGeometry. ∀b,a,c,u:Point.  (ab ⊥ cu 
⇒ ba ⊥ cu)
Proof
Definitions occuring in Statement : 
geo-perp: ab ⊥ cd
, 
basic-geometry: BasicGeometry
, 
geo-point: Point
, 
all: ∀x:A. B[x]
, 
implies: P 
⇒ Q
Definitions unfolded in proof : 
all: ∀x:A. B[x]
, 
implies: P 
⇒ Q
, 
member: t ∈ T
, 
uall: ∀[x:A]. B[x]
, 
guard: {T}
, 
and: P ∧ Q
, 
cand: A c∧ B
, 
prop: ℙ
, 
subtype_rel: A ⊆r B
, 
uimplies: b supposing a
Lemmas referenced : 
geo-perp-all-symmetry, 
geo-perp_wf, 
geo-point_wf, 
euclidean-plane-structure-subtype, 
euclidean-plane-subtype, 
basic-geometry-subtype, 
subtype_rel_transitivity, 
basic-geometry_wf, 
euclidean-plane_wf, 
euclidean-plane-structure_wf, 
geo-primitives_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
lambdaFormation_alt, 
cut, 
introduction, 
extract_by_obid, 
sqequalHypSubstitution, 
dependent_functionElimination, 
thin, 
hypothesisEquality, 
isectElimination, 
independent_functionElimination, 
hypothesis, 
productElimination, 
universeIsType, 
inhabitedIsType, 
applyEquality, 
instantiate, 
independent_isectElimination, 
sqequalRule
Latex:
\mforall{}e:BasicGeometry.  \mforall{}b,a,c,u:Point.    (ab  \mbot{}  cu  {}\mRightarrow{}  ba  \mbot{}  cu)
Date html generated:
2019_10_16-PM-01_29_26
Last ObjectModification:
2018_12_11-PM-06_11_31
Theory : euclidean!plane!geometry
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