Nuprl Lemma : not-geo-triangle-iff-colinear
∀e:HeytingGeometry. ∀a,b,c:Point. (¬a # bc ⇐⇒ Colinear(a;b;c))
Proof
Definitions occuring in Statement :
geo-triangle: a # bc,
heyting-geometry: HeytingGeometry,
geo-colinear: Colinear(a;b;c),
geo-point: Point,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
not: ¬A
Definitions unfolded in proof :
cand: A c∧ B,
and: P ∧ Q,
geo-triangle: a # bc,
heyting-geometry: HeytingGeometry,
member: t ∈ T,
all: ∀x:A. B[x]
Lemmas referenced :
heyting-geometry_wf,
euclidean-plane-axioms
Rules used in proof :
hypothesis,
productElimination,
sqequalRule,
hypothesisEquality,
thin,
dependent_functionElimination,
sqequalHypSubstitution,
extract_by_obid,
introduction,
cut,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}e:HeytingGeometry. \mforall{}a,b,c:Point. (\mneg{}a \# bc \mLeftarrow{}{}\mRightarrow{} Colinear(a;b;c))
Date html generated:
2017_10_02-PM-07_00_57
Last ObjectModification:
2017_08_06-PM-09_12_51
Theory : euclidean!plane!geometry
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