Nuprl Lemma : pgeo-psep-irrefl
∀e:ProjectivePlane. ∀[a,b:Point]. ¬a ≠ b supposing a = b ∈ Point
Proof
Definitions occuring in Statement :
projective-plane: ProjectivePlane,
pgeo-psep: a ≠ b,
pgeo-point: Point,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
not: ¬A,
equal: s = t ∈ T
Definitions unfolded in proof :
guard: {T},
subtype_rel: A ⊆r B,
prop: ℙ,
pgeo-peq: a ≡ b,
false: False,
implies: P ⇒ Q,
not: ¬A,
uimplies: b supposing a,
member: t ∈ T,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x]
Lemmas referenced :
pgeo-point_wf,
equal_wf,
pgeo-primitives_wf,
projective-plane-structure_wf,
projective-plane-structure-complete_wf,
projective-plane_wf,
subtype_rel_transitivity,
projective-plane-subtype,
projective-plane-structure-complete_subtype,
projective-plane-structure_subtype,
pgeo-psep_wf,
pgeo-peq_weakening
Rules used in proof :
equalitySymmetry,
equalityTransitivity,
isect_memberEquality,
because_Cache,
lambdaEquality,
sqequalRule,
independent_isectElimination,
instantiate,
applyEquality,
isectElimination,
voidElimination,
hypothesis,
independent_functionElimination,
hypothesisEquality,
dependent_functionElimination,
sqequalHypSubstitution,
extract_by_obid,
thin,
cut,
introduction,
isect_memberFormation,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}e:ProjectivePlane. \mforall{}[a,b:Point]. \mneg{}a \mneq{} b supposing a = b
Date html generated:
2018_05_22-PM-00_57_35
Last ObjectModification:
2018_01_08-PM-03_28_10
Theory : euclidean!plane!geometry
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