Nuprl Lemma : eu-colinear-implies-1
∀e:EuclideanPlane. ∀x,a,b:Point. (Colinear(b;a;x) ⇒ Colinear(b;a;a))
Proof
Definitions occuring in Statement :
euclidean-plane: EuclideanPlane,
eu-colinear: Colinear(a;b;c),
eu-point: Point,
all: ∀x:A. B[x],
implies: P ⇒ Q
Definitions unfolded in proof :
rev_implies: P ⇐ Q,
false: False,
not: ¬A,
iff: P ⇐⇒ Q,
cand: A c∧ B,
and: P ∧ Q,
euclidean-plane: EuclideanPlane,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
implies: P ⇒ Q,
all: ∀x:A. B[x]
Lemmas referenced :
eu-colinear_wf,
eu-point_wf,
euclidean-plane_wf,
eu-colinear-def,
not_wf,
equal_wf,
member_wf,
eu-between_wf
Rules used in proof :
productEquality,
voidElimination,
independent_pairFormation,
independent_functionElimination,
productElimination,
dependent_functionElimination,
because_Cache,
hypothesis,
hypothesisEquality,
rename,
setElimination,
thin,
isectElimination,
sqequalHypSubstitution,
lemma_by_obid,
cut,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}e:EuclideanPlane. \mforall{}x,a,b:Point. (Colinear(b;a;x) {}\mRightarrow{} Colinear(b;a;a))
Date html generated:
2016_05_18-AM-06_35_47
Last ObjectModification:
2016_01_04-AM-11_09_33
Theory : euclidean!geometry
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