Nuprl Lemma : between-preserves-left-4
∀e:EuclideanPlane. ∀A,B,C,V:Point. (C leftof AB ⇒ A-B-V ⇒ C leftof BV)
Proof
Definitions occuring in Statement :
euclidean-plane: EuclideanPlane,
geo-strict-between: a-b-c,
geo-left: a leftof bc,
geo-point: Point,
all: ∀x:A. B[x],
implies: P ⇒ Q
Definitions unfolded in proof :
uimplies: b supposing a,
guard: {T},
prop: ℙ,
subtype_rel: A ⊆r B,
cand: A c∧ B,
and: P ∧ Q,
basic-geometry: BasicGeometry,
member: t ∈ T,
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
all: ∀x:A. B[x]
Lemmas referenced :
geo-point_wf,
geo-primitives_wf,
euclidean-plane-structure_wf,
euclidean-plane_wf,
subtype_rel_transitivity,
euclidean-plane-subtype,
euclidean-plane-structure-subtype,
left-all-symmetry,
geo-strict-between_wf,
geo-left_wf,
strict-between-left-right,
geo-colinear_wf,
geo-colinear-same
Rules used in proof :
inhabitedIsType,
independent_isectElimination,
instantiate,
independent_pairFormation,
functionIsType,
dependent_functionElimination,
independent_functionElimination,
applyEquality,
universeIsType,
productIsType,
isectIsType,
because_Cache,
productElimination,
hypothesis,
hypothesisEquality,
sqequalRule,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
introduction,
cut,
lambdaFormation_alt,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}e:EuclideanPlane. \mforall{}A,B,C,V:Point. (C leftof AB {}\mRightarrow{} A-B-V {}\mRightarrow{} C leftof BV)
Date html generated:
2019_10_29-AM-09_15_21
Last ObjectModification:
2019_10_18-PM-03_15_56
Theory : euclidean!plane!geometry
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