Nuprl Lemma : geo-ge-sep
∀g:EuclideanPlane. ∀a,b,c,d:Point. (cd ≥ ab ⇒ a ≠ b ⇒ c ≠ d)
Proof
Definitions occuring in Statement :
euclidean-plane: EuclideanPlane,
geo-ge: cd ≥ ab,
geo-sep: a ≠ b,
geo-point: Point,
all: ∀x:A. B[x],
implies: P ⇒ Q
Definitions unfolded in proof :
cand: A c∧ B,
and: P ∧ Q,
member: t ∈ T,
all: ∀x:A. B[x]
Lemmas referenced :
euclidean-plane_wf,
euclidean-plane-axioms
Rules used in proof :
productElimination,
hypothesisEquality,
thin,
dependent_functionElimination,
sqequalHypSubstitution,
hypothesis,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
extract_by_obid,
introduction,
cut
Latex:
\mforall{}g:EuclideanPlane. \mforall{}a,b,c,d:Point. (cd \mgeq{} ab {}\mRightarrow{} a \mneq{} b {}\mRightarrow{} c \mneq{} d)
Date html generated:
2017_10_02-PM-03_27_49
Last ObjectModification:
2017_08_08-PM-00_35_30
Theory : euclidean!plane!geometry
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