Nuprl Lemma : geo-parallel-strict
∀e:EuclideanPlane. ∀a,b:Point. (geo-parallel(e;a;b;a;b) ⇒ False)
Proof
Definitions occuring in Statement :
geo-parallel: geo-parallel(e;a;b;c;d),
euclidean-plane: EuclideanPlane,
geo-point: Point,
all: ∀x:A. B[x],
implies: P ⇒ Q,
false: False
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
false: False,
geo-parallel: geo-parallel(e;a;b;c;d),
and: P ∧ Q,
member: t ∈ T,
uall: ∀[x:A]. B[x],
basic-geometry: BasicGeometry,
uimplies: b supposing a,
guard: {T},
prop: ℙ,
subtype_rel: A ⊆r B,
geo-eq: a ≡ b,
not: ¬A
Lemmas referenced :
geo-colinear-same,
geo-eq_weakening,
lsep-implies-sep,
geo-parallel_wf,
geo-point_wf,
euclidean-plane-structure-subtype,
euclidean-plane-subtype,
subtype_rel_transitivity,
euclidean-plane_wf,
euclidean-plane-structure_wf,
geo-primitives_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
sqequalHypSubstitution,
productElimination,
thin,
hypothesis,
dependent_functionElimination,
hypothesisEquality,
independent_functionElimination,
introduction,
extract_by_obid,
isectElimination,
sqequalRule,
because_Cache,
independent_isectElimination,
applyEquality,
instantiate
Latex:
\mforall{}e:EuclideanPlane. \mforall{}a,b:Point. (geo-parallel(e;a;b;a;b) {}\mRightarrow{} False)
Date html generated:
2018_05_22-PM-00_14_31
Last ObjectModification:
2017_10_12-PM-01_57_29
Theory : euclidean!plane!geometry
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