Nuprl Lemma : lt-angle-not-cong2
∀e:EuclideanPlane. ∀a,b,c,x,y,z:Point. (abc < xyz ⇒ (¬abc ≅a xyz))
Proof
Definitions occuring in Statement :
geo-lt-angle: abc < xyz,
geo-cong-angle: abc ≅a xyz,
euclidean-plane: EuclideanPlane,
geo-point: Point,
all: ∀x:A. B[x],
not: ¬A,
implies: P ⇒ Q
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
not: ¬A,
false: False,
member: t ∈ T,
uall: ∀[x:A]. B[x],
basic-geometry: BasicGeometry,
prop: ℙ,
subtype_rel: A ⊆r B,
guard: {T},
uimplies: b supposing a
Lemmas referenced :
geo-cong-angle_wf,
geo-lt-angle_wf,
geo-point_wf,
euclidean-plane-structure-subtype,
euclidean-plane-subtype,
subtype_rel_transitivity,
euclidean-plane_wf,
euclidean-plane-structure_wf,
geo-primitives_wf,
lt-angle-not-cong,
geo-cong-angle-preserves-lt-angle
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation_alt,
cut,
thin,
because_Cache,
hypothesis,
sqequalHypSubstitution,
independent_functionElimination,
voidElimination,
universeIsType,
introduction,
extract_by_obid,
isectElimination,
sqequalRule,
hypothesisEquality,
dependent_functionElimination,
inhabitedIsType,
applyEquality,
instantiate,
independent_isectElimination
Latex:
\mforall{}e:EuclideanPlane. \mforall{}a,b,c,x,y,z:Point. (abc < xyz {}\mRightarrow{} (\mneg{}abc \mcong{}\msuba{} xyz))
Date html generated:
2019_10_16-PM-02_00_53
Last ObjectModification:
2018_12_03-PM-01_42_34
Theory : euclidean!plane!geometry
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