Nuprl Lemma : geo-add-length-zero2
∀[e:BasicGeometry]. ∀[x:Length]. ∀[a:Point]. (x + |aa| = x ∈ Length)
Proof
Definitions occuring in Statement :
geo-add-length: p + q,
geo-length: |s|,
geo-length-type: Length,
geo-mk-seg: ab,
basic-geometry: BasicGeometry,
geo-point: Point,
uall: ∀[x:A]. B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
implies: P ⇒ Q,
rev_implies: P ⇐ Q,
and: P ∧ Q,
iff: P ⇐⇒ Q,
guard: {T},
uimplies: b supposing a,
subtype_rel: A ⊆r B,
true: True,
prop: ℙ,
squash: ↓T,
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
Error :basic-geo-primitives_wf,
Error :basic-geo-structure_wf,
subtype_rel_transitivity,
basic-geometry-subtype,
geo-point_wf,
iff_weakening_equal,
geo-length-null-segment,
basic-geometry_wf,
geo-length-type_wf,
geo-add-length_wf,
true_wf,
squash_wf,
equal_wf,
geo-add-length-zero
Rules used in proof :
instantiate,
independent_functionElimination,
productElimination,
independent_isectElimination,
baseClosed,
imageMemberEquality,
sqequalRule,
natural_numberEquality,
because_Cache,
universeEquality,
equalitySymmetry,
equalityTransitivity,
imageElimination,
lambdaEquality,
applyEquality,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
hypothesis,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
extract_by_obid,
introduction,
cut
Latex:
\mforall{}[e:BasicGeometry]. \mforall{}[x:Length]. \mforall{}[a:Point]. (x + |aa| = x)
Date html generated:
2017_10_02-PM-06_13_48
Last ObjectModification:
2017_08_05-PM-04_10_56
Theory : euclidean!plane!geometry
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