Nuprl Lemma : geo-lt-implies-gt-strong
∀g:EuclideanPlane. ∀a,b,c,d:Point. (|cd| < |ab| ⇒ ab > cd)
Proof
Definitions occuring in Statement :
geo-lt: p < q,
geo-length: |s|,
geo-mk-seg: ab,
euclidean-plane: EuclideanPlane,
geo-gt: cd > ab,
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,
geo-gt: cd > ab,
squash: ↓T,
uall: ∀[x:A]. B[x],
basic-geometry: BasicGeometry,
euclidean-plane: EuclideanPlane,
prop: ℙ,
subtype_rel: A ⊆r B,
guard: {T},
uimplies: b supposing a
Lemmas referenced :
geo-lt-implies-gt-strong-1,
geo-lt_wf,
geo-length_wf,
geo-mk-seg_wf,
geo-point_wf,
euclidean-plane-structure-subtype,
euclidean-plane-subtype,
subtype_rel_transitivity,
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,
independent_functionElimination,
hypothesis,
sqequalRule,
imageMemberEquality,
baseClosed,
universeIsType,
isectElimination,
setElimination,
rename,
inhabitedIsType,
applyEquality,
instantiate,
independent_isectElimination
Latex:
\mforall{}g:EuclideanPlane. \mforall{}a,b,c,d:Point. (|cd| < |ab| {}\mRightarrow{} ab > cd)
Date html generated:
2019_10_16-PM-01_36_39
Last ObjectModification:
2018_12_11-PM-01_27_14
Theory : euclidean!plane!geometry
Home
Index