Nuprl Lemma : pgeo-psep-or
∀g:ProjectivePlane. ∀p,q,r:Point. (p ≠ q ⇒ {p ≠ r ∨ r ≠ q})
Proof
Definitions occuring in Statement :
projective-plane: ProjectivePlane,
pgeo-psep: a ≠ b,
pgeo-point: Point,
guard: {T},
all: ∀x:A. B[x],
implies: P ⇒ Q,
or: P ∨ Q
Definitions unfolded in proof :
uimplies: b supposing a,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
prop: ℙ,
or: P ∨ Q,
projective-plane: ProjectivePlane,
member: t ∈ T,
and: P ∧ Q,
guard: {T},
exists: ∃x:A. B[x],
pgeo-psep: a ≠ b,
implies: P ⇒ Q,
all: ∀x:A. B[x]
Lemmas referenced :
pgeo-point_wf,
pgeo-primitives_wf,
projective-plane-structure_wf,
basic-projective-plane_wf,
projective-plane_wf,
subtype_rel_transitivity,
projective-plane-subtype,
basic-projective-plane-subtype,
projective-plane-structure_subtype,
pgeo-psep_wf,
pgeo-plsep-to-psep,
LP-sep-or2
Rules used in proof :
independent_isectElimination,
instantiate,
inrFormation,
sqequalRule,
applyEquality,
isectElimination,
inlFormation,
because_Cache,
unionElimination,
independent_functionElimination,
hypothesisEquality,
rename,
setElimination,
dependent_functionElimination,
extract_by_obid,
introduction,
thin,
productElimination,
sqequalHypSubstitution,
hypothesis,
cut,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}g:ProjectivePlane. \mforall{}p,q,r:Point. (p \mneq{} q {}\mRightarrow{} \{p \mneq{} r \mvee{} r \mneq{} q\})
Date html generated:
2018_05_22-PM-00_43_45
Last ObjectModification:
2017_11_17-AM-11_59_04
Theory : euclidean!plane!geometry
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