Nuprl Lemma : geo-cong-implies-ge
∀e:BasicGeometry. ∀a,b,c,d:Point. (ab ≅ cd ⇒ cd ≥ ab)
Proof
Definitions occuring in Statement :
basic-geometry: BasicGeometry,
geo-ge: cd ≥ ab,
geo-congruent: ab ≅ cd,
geo-point: Point,
all: ∀x:A. B[x],
implies: P ⇒ Q
Definitions unfolded in proof :
guard: {T},
subtype_rel: A ⊆r B,
prop: ℙ,
uimplies: b supposing a,
member: t ∈ T,
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
all: ∀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-congruent_wf,
geo-congruent-symmetry,
geo-congruent-implies-ge
Rules used in proof :
sqequalRule,
instantiate,
applyEquality,
hypothesis,
dependent_functionElimination,
independent_isectElimination,
because_Cache,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
introduction,
cut,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}e:BasicGeometry. \mforall{}a,b,c,d:Point. (ab \00D0 cd {}\mRightarrow{} cd \mgeq{} ab)
Date html generated:
2017_10_02-PM-04_43_32
Last ObjectModification:
2017_08_05-AM-09_07_59
Theory : euclidean!plane!geometry
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