Nuprl Lemma : pgeo-peq_transitivity
∀g:ProjectivePlane. ∀a,b,c:Point. (a ≡ b ⇒ b ≡ c ⇒ a ≡ c)
Proof
Definitions occuring in Statement :
projective-plane: ProjectivePlane,
pgeo-peq: a ≡ b,
pgeo-point: Point,
all: ∀x:A. B[x],
implies: P ⇒ Q
Definitions unfolded in proof :
uimplies: b supposing a,
guard: {T},
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
prop: ℙ,
false: False,
pgeo-incident: a I b,
member: t ∈ T,
and: P ∧ Q,
exists: ∃x:A. B[x],
pgeo-psep: a ≠ b,
not: ¬A,
pgeo-peq: 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-peq_wf,
pgeo-psep_wf,
pgeo-peq-preserves-incidence
Rules used in proof :
independent_isectElimination,
instantiate,
sqequalRule,
applyEquality,
isectElimination,
voidElimination,
because_Cache,
hypothesis,
independent_functionElimination,
hypothesisEquality,
dependent_functionElimination,
extract_by_obid,
introduction,
cut,
thin,
productElimination,
sqequalHypSubstitution,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}g:ProjectivePlane. \mforall{}a,b,c:Point. (a \mequiv{} b {}\mRightarrow{} b \mequiv{} c {}\mRightarrow{} a \mequiv{} c)
Date html generated:
2018_05_22-PM-00_46_08
Last ObjectModification:
2017_11_20-AM-09_45_22
Theory : euclidean!plane!geometry
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