Nuprl Lemma : eu-lt-null-segment2
∀e:EuclideanPlane. ∀[p:{p:Point| O_X_p} ]. ∀[a,b:Point]. (False) supposing ((a = b ∈ Point) and p < |ab|)
Proof
Definitions occuring in Statement :
eu-lt: p < q,
eu-length: |s|,
eu-mk-seg: ab,
euclidean-plane: EuclideanPlane,
eu-between-eq: a_b_c,
eu-X: X,
eu-O: O,
eu-point: Point,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
false: False,
set: {x:A| B[x]} ,
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
false: False,
prop: ℙ,
euclidean-plane: EuclideanPlane,
so_lambda: λ2x.t[x],
so_apply: x[s],
uiff: uiff(P;Q),
and: P ∧ Q
Lemmas referenced :
eu-lt_wf,
eu-between-eq_wf,
eu-O_wf,
eu-X_wf,
eu-length_wf,
eu-mk-seg_wf,
equal_wf,
eu-point_wf,
set_wf,
euclidean-plane_wf,
eu-lt-null-segment
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
isect_memberFormation,
introduction,
cut,
hypothesis,
equalitySymmetry,
thin,
hyp_replacement,
Error :applyLambdaEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
setElimination,
rename,
dependent_set_memberEquality,
because_Cache,
dependent_functionElimination,
sqequalRule,
isect_memberEquality,
equalityTransitivity,
voidElimination,
lambdaEquality,
productElimination,
independent_isectElimination
Latex:
\mforall{}e:EuclideanPlane. \mforall{}[p:\{p:Point| O\_X\_p\} ]. \mforall{}[a,b:Point]. (False) supposing ((a = b) and p < |ab|)
Date html generated:
2016_10_26-AM-07_42_06
Last ObjectModification:
2016_07_12-AM-08_08_17
Theory : euclidean!geometry
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