Nuprl Lemma : geo-perp-in-symmetry1
∀e:BasicGeometry. ∀x:Point. ∀[a,b,c,d:Point]. (ab ⊥x cd ⇒ cd ⊥x ab)
Proof
Definitions occuring in Statement :
geo-perp-in: ab ⊥x cd,
basic-geometry: BasicGeometry,
geo-point: Point,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q
Definitions unfolded in proof :
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
geo-perp-in: ab ⊥x cd,
and: P ∧ Q,
cand: A c∧ B,
member: t ∈ T,
prop: ℙ,
subtype_rel: A ⊆r B,
guard: {T},
uimplies: b supposing a
Lemmas referenced :
right-angle-symmetry,
geo-colinear_wf,
geo-perp-in_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,
isect_memberFormation,
sqequalHypSubstitution,
productElimination,
thin,
cut,
hypothesis,
independent_pairFormation,
dependent_functionElimination,
hypothesisEquality,
independent_functionElimination,
introduction,
extract_by_obid,
isectElimination,
applyEquality,
because_Cache,
sqequalRule,
instantiate,
independent_isectElimination
Latex:
\mforall{}e:BasicGeometry. \mforall{}x:Point. \mforall{}[a,b,c,d:Point]. (ab \mbot{}x cd {}\mRightarrow{} cd \mbot{}x ab)
Date html generated:
2018_05_22-PM-00_04_06
Last ObjectModification:
2018_04_18-PM-09_47_08
Theory : euclidean!plane!geometry
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