Nuprl Lemma : pgeo-leq-equiv
∀g:ProjectivePlane. EquivRel(Line;p,q.p ≡ q)
Proof
Definitions occuring in Statement :
projective-plane: ProjectivePlane,
pgeo-leq: a ≡ b,
pgeo-line: Line,
equiv_rel: EquivRel(T;x,y.E[x; y]),
all: ∀x:A. B[x]
Definitions unfolded in proof :
trans: Trans(T;x,y.E[x; y]),
prop: ℙ,
sym: Sym(T;x,y.E[x; y]),
cand: A c∧ B,
uimplies: b supposing a,
guard: {T},
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
member: t ∈ T,
refl: Refl(T;x,y.E[x; y]),
and: P ∧ Q,
equiv_rel: EquivRel(T;x,y.E[x; y]),
all: ∀x:A. B[x]
Lemmas referenced :
pgeo-leq_transitivity,
pgeo-leq_wf,
pgeo-leq_inversion,
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-line_wf,
pgeo-leq_weakening
Rules used in proof :
sqequalRule,
independent_isectElimination,
instantiate,
applyEquality,
isectElimination,
hypothesis,
independent_functionElimination,
because_Cache,
hypothesisEquality,
thin,
dependent_functionElimination,
sqequalHypSubstitution,
extract_by_obid,
introduction,
cut,
independent_pairFormation,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}g:ProjectivePlane. EquivRel(Line;p,q.p \mequiv{} q)
Date html generated:
2018_05_22-PM-00_45_18
Last ObjectModification:
2018_01_03-PM-03_42_30
Theory : euclidean!plane!geometry
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