Nuprl Lemma : euclid-P1-ext
∀e:EuclideanPlane. ∀A,B:Point. ∃C:Point. (AC=AB ∧ BC=AB ∧ AC=BC) supposing ¬(A = B ∈ Point)
Proof
Definitions occuring in Statement :
euclidean-plane: EuclideanPlane,
eu-congruent: ab=cd,
eu-point: Point,
uimplies: b supposing a,
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
not: ¬A,
and: P ∧ Q,
equal: s = t ∈ T
Definitions unfolded in proof :
spreadn: spread7,
stable__eu-congruent,
sq_stable__from_stable,
sq_stable__eu-congruent,
eu-seg-congruent-iff-length,
eu-congruent-iff-length,
record-select: r.x,
eu-extend: (extend ab by cd),
eu-extend-exists,
uimplies: b supposing a,
so_apply: x[s1;s2],
top: Top,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2;s3;s4],
so_lambda: so_lambda(x,y,z,w.t[x; y; z; w]),
uall: ∀[x:A]. B[x],
circle-circle-continuity1,
euclid-P1,
member: t ∈ T
Lemmas referenced :
stable__eu-congruent,
sq_stable__from_stable,
sq_stable__eu-congruent,
eu-seg-congruent-iff-length,
eu-congruent-iff-length,
eu-extend-exists,
circle-circle-continuity1,
euclid-P1
Rules used in proof :
equalitySymmetry,
equalityTransitivity,
independent_isectElimination,
voidEquality,
voidElimination,
isect_memberEquality,
baseClosed,
isectElimination,
sqequalHypSubstitution,
thin,
sqequalRule,
hypothesis,
extract_by_obid,
instantiate,
cut,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
introduction
Latex:
\mforall{}e:EuclideanPlane. \mforall{}A,B:Point. \mexists{}C:Point. (AC=AB \mwedge{} BC=AB \mwedge{} AC=BC) supposing \mneg{}(A = B)
Date html generated:
2016_07_08-PM-05_54_28
Last ObjectModification:
2016_07_05-PM-03_04_23
Theory : euclidean!geometry
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