Nuprl Lemma : geo-eq-x-implies-eq
∀e:BasicGeometry. ∀a,b:Point. ((X = |ab| ∈ Length) ⇒ a ≡ b)
Proof
Definitions occuring in Statement :
geo-length: |s|,
geo-length-type: Length,
geo-mk-seg: ab,
basic-geometry: BasicGeometry,
geo-X: X,
geo-eq: a ≡ b,
geo-point: Point,
all: ∀x:A. B[x],
implies: P ⇒ Q,
equal: s = t ∈ T
Definitions unfolded in proof :
uimplies: b supposing a,
guard: {T},
subtype_rel: A ⊆r B,
basic-geometry: BasicGeometry,
prop: ℙ,
implies: P ⇒ Q,
member: t ∈ T,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
and: P ∧ Q,
uiff: uiff(P;Q)
Lemmas referenced :
Error :basic-geo-primitives_wf,
Error :basic-geo-structure_wf,
basic-geometry_wf,
subtype_rel_transitivity,
basic-geometry-subtype,
geo-point_wf,
geo-mk-seg_wf,
geo-length_wf,
geo-length-type_wf,
equal_wf,
geo-length-null-segment,
geo-congruent-iff-length,
geo-congruence-identity
Rules used in proof :
sqequalRule,
independent_isectElimination,
instantiate,
applyEquality,
rename,
setElimination,
because_Cache,
equalitySymmetry,
equalityTransitivity,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
hypothesis,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
extract_by_obid,
introduction,
cut,
productElimination,
dependent_functionElimination,
independent_functionElimination
Latex:
\mforall{}e:BasicGeometry. \mforall{}a,b:Point. ((X = |ab|) {}\mRightarrow{} a \mequiv{} b)
Date html generated:
2017_10_02-PM-06_36_32
Last ObjectModification:
2017_08_05-PM-04_45_32
Theory : euclidean!plane!geometry
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