Nuprl Lemma : geo-line-eq-equiv
∀g:EuclideanPlane. EquivRel(Line;l,m.l ≡ m)
Proof
Definitions occuring in Statement :
geo-line-eq: l ≡ m,
geo-line: Line,
euclidean-plane: EuclideanPlane,
equiv_rel: EquivRel(T;x,y.E[x; y]),
all: ∀x:A. B[x]
Definitions unfolded in proof :
all: ∀x:A. B[x],
equiv_rel: EquivRel(T;x,y.E[x; y]),
and: P ∧ Q,
refl: Refl(T;x,y.E[x; y]),
member: t ∈ T,
implies: P ⇒ Q,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
guard: {T},
uimplies: b supposing a,
cand: A c∧ B,
sym: Sym(T;x,y.E[x; y]),
prop: ℙ,
trans: Trans(T;x,y.E[x; y])
Lemmas referenced :
geo-line-eq_weakening,
geo-line_wf,
euclidean-plane-structure-subtype,
euclidean-plane-subtype,
subtype_rel_transitivity,
euclidean-plane_wf,
euclidean-plane-structure_wf,
geo-primitives_wf,
geo-line-eq_inversion,
geo-line-eq_wf,
geo-line-eq_transitivity
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
independent_pairFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
because_Cache,
independent_functionElimination,
hypothesis,
applyEquality,
instantiate,
isectElimination,
independent_isectElimination,
sqequalRule
Latex:
\mforall{}g:EuclideanPlane. EquivRel(Line;l,m.l \mequiv{} m)
Date html generated:
2018_05_22-PM-01_02_34
Last ObjectModification:
2018_05_10-PM-04_28_36
Theory : euclidean!plane!geometry
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