Nuprl Lemma : geo-le-iff-between
∀g:EuclideanPlane. ∀s1,s2:geo-segment(g). (|s1| ≤ |s2| ⇐⇒ X_|s1|_|s2|)
Proof
Definitions occuring in Statement :
geo-le: p ≤ q,
geo-length: |s|,
geo-segment: geo-segment(e),
geo-X: X,
euclidean-plane: EuclideanPlane,
geo-between: a_b_c,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
basic-geometry: BasicGeometry,
euclidean-plane: EuclideanPlane
Lemmas referenced :
geo-le-iff-between-points,
geo-length_wf1,
geo-segment_wf,
euclidean-plane_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation_alt,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
isectElimination,
sqequalRule,
hypothesis,
inhabitedIsType,
universeIsType,
setElimination,
rename
Latex:
\mforall{}g:EuclideanPlane. \mforall{}s1,s2:geo-segment(g). (|s1| \mleq{} |s2| \mLeftarrow{}{}\mRightarrow{} X\_|s1|\_|s2|)
Date html generated:
2019_10_16-PM-01_34_13
Last ObjectModification:
2018_10_03-AM-11_18_12
Theory : euclidean!plane!geometry
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