Nuprl Lemma : left-not-between
∀g:EuclideanPlane. ∀a,b,c:Point. (a leftof cb ⇒ (¬a_b_c))
Proof
Definitions occuring in Statement :
euclidean-plane: EuclideanPlane,
geo-left: a leftof bc,
geo-between: a_b_c,
geo-point: Point,
all: ∀x:A. B[x],
not: ¬A,
implies: P ⇒ Q
Definitions unfolded in proof :
true: True,
or: P ∨ Q,
uimplies: b supposing a,
guard: {T},
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
false: False,
not: ¬A,
implies: P ⇒ Q,
all: ∀x:A. B[x],
cand: A c∧ B,
and: P ∧ Q,
geo-eq: a ≡ b
Lemmas referenced :
minimal-not-not-excluded-middle,
minimal-double-negation-hyp-elim,
true_wf,
geo-sep_wf,
or_wf,
false_wf,
geo-point_wf,
geo-left_wf,
geo-primitives_wf,
euclidean-plane-structure_wf,
euclidean-plane_wf,
subtype_rel_transitivity,
euclidean-plane-subtype,
euclidean-plane-structure-subtype,
geo-between_wf,
left-convex,
left-implies-sep,
geo-sep-sym,
left-symmetry,
geo-sep-irrefl2,
geo-between-trivial
Rules used in proof :
natural_numberEquality,
unionElimination,
functionEquality,
sqequalRule,
independent_isectElimination,
instantiate,
applyEquality,
hypothesisEquality,
isectElimination,
extract_by_obid,
introduction,
voidElimination,
independent_functionElimination,
sqequalHypSubstitution,
hypothesis,
because_Cache,
thin,
cut,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
productElimination,
dependent_functionElimination,
independent_pairFormation,
inrFormation,
productEquality,
inlFormation
Latex:
\mforall{}g:EuclideanPlane. \mforall{}a,b,c:Point. (a leftof cb {}\mRightarrow{} (\mneg{}a\_b\_c))
Date html generated:
2017_10_02-PM-04_40_31
Last ObjectModification:
2017_08_08-PM-01_49_39
Theory : euclidean!plane!geometry
Home
Index