Nuprl Lemma : geo-perp-irrefl
∀[e:BasicGeometry]. ∀[a,b:Point]. (ab ⊥ ab ⇒ a ≡ b)
Proof
Definitions occuring in Statement :
geo-perp: ab ⊥ cd,
basic-geometry: BasicGeometry,
geo-eq: a ≡ b,
geo-point: Point,
uall: ∀[x:A]. B[x],
implies: P ⇒ Q
Definitions unfolded in proof :
subtype_rel: A ⊆r B,
false: False,
not: ¬A,
geo-eq: a ≡ b,
prop: ℙ,
uimplies: b supposing a,
guard: {T},
geo-perp-in: ab ⊥x cd,
all: ∀x:A. B[x],
cand: A c∧ B,
and: P ∧ Q,
exists: ∃x:A. B[x],
geo-perp: ab ⊥ cd,
implies: P ⇒ Q,
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
geo-point_wf,
Error :basic-geo-primitives_wf,
Error :basic-geo-structure_wf,
basic-geometry_wf,
subtype_rel_transitivity,
basic-geometry-subtype,
geo-sep_wf,
geo-perp_wf,
geo-eq_transitivity,
geo-eq_inversion,
geo-colinear-same,
right-angle-legs-same
Rules used in proof :
voidElimination,
isect_memberEquality,
instantiate,
applyEquality,
lambdaEquality,
sqequalRule,
independent_isectElimination,
independent_pairFormation,
isectElimination,
because_Cache,
hypothesis,
independent_functionElimination,
hypothesisEquality,
dependent_functionElimination,
extract_by_obid,
thin,
productElimination,
sqequalHypSubstitution,
lambdaFormation,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[e:BasicGeometry]. \mforall{}[a,b:Point]. (ab \mbot{} ab {}\mRightarrow{} a \mequiv{} b)
Date html generated:
2017_10_02-PM-06_43_35
Last ObjectModification:
2017_08_05-PM-04_49_31
Theory : euclidean!plane!geometry
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