Nuprl Lemma : geo-perp-symmetry
∀e:BasicGeometry. ∀a,b,c,d:Point. (ab ⊥ cd ⇒ cd ⊥ ab)
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{}a,b,c,d:Point. (ab \mbot{} cd {}\mRightarrow{} cd \mbot{} ab)
Date html generated:
2019_10_16-PM-01_29_15
Last ObjectModification:
2018_12_11-PM-06_11_25
Theory : euclidean!plane!geometry
Home
Index