Nuprl Lemma : geo-lt-null-segment2
∀e:BasicGeometry. ∀[p:Length]. ∀[a,b:Point]. (False) supposing (a ≡ b and p < |ab|)
Proof
Definitions occuring in Statement :
geo-lt: p < q,
geo-length: |s|,
geo-length-type: Length,
geo-mk-seg: ab,
basic-geometry: BasicGeometry,
geo-eq: a ≡ b,
geo-point: Point,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
false: False
Definitions unfolded in proof :
basic-geometry: BasicGeometry,
guard: {T},
subtype_rel: A ⊆r B,
prop: ℙ,
false: False,
uimplies: b supposing a,
member: t ∈ T,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
not: ¬A,
geo-eq: a ≡ b,
and: P ∧ Q,
iff: P ⇐⇒ Q
Lemmas referenced :
geo-length-type_wf,
geo-point_wf,
geo-mk-seg_wf,
geo-length_wf,
geo-lt_wf,
Error :basic-geo-primitives_wf,
Error :basic-geo-structure_wf,
basic-geometry_wf,
subtype_rel_transitivity,
basic-geometry-subtype,
geo-eq_wf,
geo-zero-le,
geo-zero-length_wf,
geo-lt_transitivity,
geo-zero-lt-iff
Rules used in proof :
voidElimination,
rename,
setElimination,
equalitySymmetry,
equalityTransitivity,
isect_memberEquality,
independent_isectElimination,
instantiate,
applyEquality,
hypothesisEquality,
thin,
isectElimination,
extract_by_obid,
because_Cache,
sqequalHypSubstitution,
sqequalRule,
hypothesis,
cut,
introduction,
isect_memberFormation,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
independent_functionElimination,
dependent_functionElimination,
productElimination
Latex:
\mforall{}e:BasicGeometry. \mforall{}[p:Length]. \mforall{}[a,b:Point]. (False) supposing (a \mequiv{} b and p < |ab|)
Date html generated:
2017_10_02-PM-06_19_25
Last ObjectModification:
2017_08_05-PM-04_13_52
Theory : euclidean!plane!geometry
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