Nuprl Lemma : geo-out-distinct
∀e:BasicGeometry. ∀a,b,c:Point. (out(a bc) ⇒ {a ≠ b ∧ a ≠ c})
Proof
Definitions occuring in Statement :
geo-out: out(p ab),
basic-geometry: BasicGeometry,
geo-sep: a ≠ b,
geo-point: Point,
guard: {T},
all: ∀x:A. B[x],
implies: P ⇒ Q,
and: P ∧ Q
Definitions unfolded in proof :
uimplies: b supposing a,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
and: P ∧ Q,
guard: {T},
geo-out: out(p ab),
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-out_wf
Rules used in proof :
because_Cache,
sqequalRule,
independent_isectElimination,
instantiate,
applyEquality,
hypothesisEquality,
isectElimination,
extract_by_obid,
introduction,
cut,
hypothesis,
thin,
productElimination,
independent_pairFormation,
sqequalHypSubstitution,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}e:BasicGeometry. \mforall{}a,b,c:Point. (out(a bc) {}\mRightarrow{} \{a \mneq{} b \mwedge{} a \mneq{} c\})
Date html generated:
2017_10_02-PM-06_26_42
Last ObjectModification:
2017_08_05-PM-04_20_15
Theory : euclidean!plane!geometry
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