Nuprl Lemma : proj-line-sep-irrefl
∀e:EuclideanParPlane. ∀x:Line?. (¬proj-line-sep(e;x;x))
Proof
Definitions occuring in Statement :
proj-line-sep: proj-line-sep(eu;l;m),
euclidean-parallel-plane: EuclideanParPlane,
geo-line: Line,
all: ∀x:A. B[x],
not: ¬A,
unit: Unit,
union: left + right
Definitions unfolded in proof :
euclidean-parallel-plane: EuclideanParPlane,
geo-line-eq: l ≡ m,
uimplies: b supposing a,
guard: {T},
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
proj-line-sep: proj-line-sep(eu;l;m),
false: False,
implies: P ⇒ Q,
not: ¬A,
all: ∀x:A. B[x]
Lemmas referenced :
geo-line-eq_weakening,
unit_wf2,
geo-primitives_wf,
euclidean-plane-structure_wf,
euclidean-plane_wf,
euclidean-parallel-plane_wf,
subtype_rel_transitivity,
euclidean-planes-subtype,
euclidean-plane-subtype,
euclidean-plane-structure-subtype,
geo-line_wf,
proj-line-sep_wf,
false_wf
Rules used in proof :
because_Cache,
rename,
setElimination,
independent_isectElimination,
instantiate,
applyEquality,
dependent_functionElimination,
unionEquality,
hypothesisEquality,
isectElimination,
independent_functionElimination,
hypothesis,
extract_by_obid,
introduction,
voidElimination,
sqequalHypSubstitution,
sqequalRule,
unionElimination,
thin,
cut,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}e:EuclideanParPlane. \mforall{}x:Line?. (\mneg{}proj-line-sep(e;x;x))
Date html generated:
2018_05_22-PM-01_14_58
Last ObjectModification:
2018_05_21-PM-05_42_07
Theory : euclidean!plane!geometry
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