Nuprl Lemma : eu-add-length-zero2
∀[e:EuclideanPlane]. ∀[x:{p:Point| O_X_p} ]. ∀[a:Point]. (x + |aa| = x ∈ {p:Point| O_X_p} )
Proof
Definitions occuring in Statement :
eu-add-length: 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,
uall: ∀[x:A]. B[x],
set: {x:A| B[x]} ,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
euclidean-plane: EuclideanPlane,
all: ∀x:A. B[x],
prop: ℙ,
squash: ↓T,
true: True,
uimplies: b supposing a,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q
Lemmas referenced :
iff_weakening_equal,
eu-length-null-segment,
euclidean-plane_wf,
true_wf,
squash_wf,
eu-add-length_wf,
eu-X_wf,
eu-O_wf,
eu-between-eq_wf,
eu-point_wf,
eu-add-length-zero
Rules used in proof :
cut,
lemma_by_obid,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
equalityEquality,
setEquality,
setElimination,
rename,
dependent_functionElimination,
applyEquality,
lambdaEquality,
imageElimination,
equalityTransitivity,
equalitySymmetry,
because_Cache,
natural_numberEquality,
sqequalRule,
imageMemberEquality,
baseClosed,
independent_isectElimination,
productElimination,
independent_functionElimination
Latex:
\mforall{}[e:EuclideanPlane]. \mforall{}[x:\{p:Point| O\_X\_p\} ]. \mforall{}[a:Point]. (x + |aa| = x)
Date html generated:
2016_05_18-AM-06_38_17
Last ObjectModification:
2016_01_16-PM-10_29_51
Theory : euclidean!geometry
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