Nuprl Lemma : geo-length-flip
∀e:BasicGeometry. ∀[a,b:Point]. (|ab| = |ba| ∈ Length)
Proof
Definitions occuring in Statement :
geo-length: |s|,
geo-length-type: Length,
geo-mk-seg: ab,
basic-geometry: BasicGeometry,
geo-point: Point,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
implies: P ⇒ Q,
so_apply: x[s1;s2],
uimplies: b supposing a,
guard: {T},
so_lambda: λ2x y.t[x; y],
prop: ℙ,
basic-geometry: BasicGeometry,
subtype_rel: A ⊆r B,
geo-length-type: Length,
member: t ∈ T,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x]
Lemmas referenced :
geo-length-flip-eq,
geo-mk-seg_wf,
geo-length_wf1,
geo-length-equiv,
Error :basic-geo-primitives_wf,
Error :basic-geo-structure_wf,
basic-geometry_wf,
subtype_rel_transitivity,
basic-geometry-subtype,
geo-eq_wf,
geo-X_wf,
geo-O_wf,
geo-between_wf,
geo-point_wf,
quotient-member-eq
Rules used in proof :
axiomEquality,
isect_memberEquality,
independent_functionElimination,
independent_isectElimination,
instantiate,
lambdaEquality,
rename,
setElimination,
dependent_functionElimination,
hypothesis,
because_Cache,
applyEquality,
hypothesisEquality,
setEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
sqequalRule,
cut,
introduction,
isect_memberFormation,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}e:BasicGeometry. \mforall{}[a,b:Point]. (|ab| = |ba|)
Date html generated:
2017_10_02-PM-04_53_02
Last ObjectModification:
2017_08_05-AM-09_10_37
Theory : euclidean!plane!geometry
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