Nuprl Lemma : geo-le-pt-right-comm
∀e:BasicGeometry. ∀a,b,c,d:Point. (a ≠ b ⇒ ab≤cd ⇒ ab≤dc)
Proof
Definitions occuring in Statement :
geo-le-pt: ab≤cd,
basic-geometry: BasicGeometry,
geo-sep: a ≠ b,
geo-point: Point,
all: ∀x:A. B[x],
implies: P ⇒ Q
Definitions unfolded in proof :
uimplies: b supposing a,
guard: {T},
subtype_rel: A ⊆r B,
basic-geometry: BasicGeometry,
uall: ∀[x:A]. B[x],
prop: ℙ,
implies: P ⇒ Q,
all: ∀x:A. B[x],
member: t ∈ T
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-le-pt_wf,
geo-le-pt-transitivity,
geo-le-pt-comm
Rules used in proof :
because_Cache,
sqequalRule,
independent_isectElimination,
instantiate,
applyEquality,
rename,
setElimination,
isectElimination,
independent_functionElimination,
thin,
dependent_functionElimination,
sqequalHypSubstitution,
extract_by_obid,
introduction,
cut,
lambdaFormation,
hypothesis,
hypothesisEquality,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}e:BasicGeometry. \mforall{}a,b,c,d:Point. (a \mneq{} b {}\mRightarrow{} ab\mleq{}cd {}\mRightarrow{} ab\mleq{}dc)
Date html generated:
2017_10_02-PM-06_46_59
Last ObjectModification:
2017_08_05-PM-04_51_47
Theory : euclidean!plane!geometry
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