Nuprl Lemma : colinear-lsep
∀g:EuclideanPlane. ∀a,b,c,y:Point. (a # bc ⇒ y ≠ b ⇒ Colinear(y;a;b) ⇒ y # bc)
Proof
Definitions occuring in Statement :
euclidean-plane: EuclideanPlane,
geo-lsep: a # bc,
geo-colinear: Colinear(a;b;c),
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,y:Point. (a \# bc {}\mRightarrow{} y \mneq{} b {}\mRightarrow{} Colinear(y;a;b) {}\mRightarrow{} y \# bc)
Date html generated:
2017_10_02-PM-03_29_23
Last ObjectModification:
2017_08_07-AM-10_47_12
Theory : euclidean!plane!geometry
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