Nuprl Lemma : geo-colinear-implies-1
∀e:BasicGeometry. ∀x,a,b:Point. (Colinear(b;a;x) ⇒ Colinear(b;a;a))
Proof
Definitions occuring in Statement :
basic-geometry: BasicGeometry,
geo-colinear: Colinear(a;b;c),
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,
prop: ℙ,
and: P ∧ Q,
member: t ∈ T,
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
all: ∀x:A. B[x]
Lemmas referenced :
Error :basic-geo-primitives_wf,
Error :basic-geo-structure_wf,
basic-geometry_wf,
subtype_rel_transitivity,
basic-geometry-subtype,
geo-point_wf,
geo-colinear_wf,
geo-colinear-same
Rules used in proof :
because_Cache,
sqequalRule,
independent_isectElimination,
instantiate,
applyEquality,
rename,
setElimination,
hypothesis,
productElimination,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
introduction,
cut,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}e:BasicGeometry. \mforall{}x,a,b:Point. (Colinear(b;a;x) {}\mRightarrow{} Colinear(b;a;a))
Date html generated:
2017_10_02-PM-04_43_53
Last ObjectModification:
2017_08_05-AM-09_08_30
Theory : euclidean!plane!geometry
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