Nuprl Lemma : geo-colinear-trivial
∀e:BasicGeometry. ∀a,b:Point. ((¬(a = b ∈ Point)) ⇒ (Colinear(a;b;b) ∧ Colinear(b;a;b)))
Proof
Definitions occuring in Statement :
basic-geometry: BasicGeometry,
geo-colinear: Colinear(a;b;c),
geo-point: Point,
all: ∀x:A. B[x],
not: ¬A,
implies: P ⇒ Q,
and: P ∧ Q,
equal: s = t ∈ T
Definitions unfolded in proof :
uimplies: b supposing a,
guard: {T},
subtype_rel: A ⊆r B,
prop: ℙ,
member: t ∈ T,
uall: ∀[x:A]. B[x],
cand: A c∧ B,
and: P ∧ Q,
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,
equal_wf,
not_wf,
geo-colinear-same
Rules used in proof :
sqequalRule,
independent_isectElimination,
instantiate,
applyEquality,
because_Cache,
independent_pairFormation,
hypothesis,
productElimination,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
introduction,
cut,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}e:BasicGeometry. \mforall{}a,b:Point. ((\mneg{}(a = b)) {}\mRightarrow{} (Colinear(a;b;b) \mwedge{} Colinear(b;a;b)))
Date html generated:
2017_10_02-PM-06_37_14
Last ObjectModification:
2017_08_05-PM-04_46_11
Theory : euclidean!plane!geometry
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