Nuprl Lemma : eu-extend-exists
∀e:EuclideanPlane. ∀q:Point. ∀a:{a:Point| ¬(q = a ∈ Point)} . ∀b,c:Point. ∃x:Point. (q_a_x ∧ ax=bc)
Proof
Definitions occuring in Statement :
euclidean-plane: EuclideanPlane,
eu-between-eq: a_b_c,
eu-congruent: ab=cd,
eu-point: Point,
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
not: ¬A,
and: P ∧ Q,
set: {x:A| B[x]} ,
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
euclidean-plane: EuclideanPlane,
and: P ∧ Q,
cand: A c∧ B,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
eu-extend_wf,
eu-extend-property,
and_wf,
eu-between-eq_wf,
eu-congruent_wf,
eu-point_wf,
set_wf,
not_wf,
equal_wf,
euclidean-plane_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
dependent_pairFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
setElimination,
rename,
hypothesisEquality,
hypothesis,
dependent_functionElimination,
because_Cache,
productElimination,
independent_pairFormation,
sqequalRule,
lambdaEquality
Latex:
\mforall{}e:EuclideanPlane. \mforall{}q:Point. \mforall{}a:\{a:Point| \mneg{}(q = a)\} . \mforall{}b,c:Point. \mexists{}x:Point. (q\_a\_x \mwedge{} ax=bc)
Date html generated:
2016_05_18-AM-06_33_45
Last ObjectModification:
2015_12_28-AM-09_28_01
Theory : euclidean!geometry
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