Nuprl Lemma : symmetry_preserves_midpoint
∀e:BasicGeometry. ∀a,b,c,d,e1,f,z:Point. ((((a=z=d ∧ b=z=e1) ∧ c=z=f) ∧ a=b=c) ⇒ d=e1=f)
Proof
Definitions occuring in Statement :
geo-midpoint: a=m=b,
basic-geometry: BasicGeometry,
geo-point: Point,
all: ∀x:A. B[x],
implies: P ⇒ Q,
and: P ∧ Q
Definitions unfolded in proof :
uimplies: b supposing a,
guard: {T},
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
and: P ∧ Q,
implies: P ⇒ Q,
all: ∀x:A. B[x],
geo-midpoint: a=m=b,
cand: A c∧ B
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-midpoint_wf,
geo-midpoint-diagonals-between,
geo-midpoint-diagonals-congruent2
Rules used in proof :
because_Cache,
sqequalRule,
independent_isectElimination,
instantiate,
applyEquality,
hypothesis,
hypothesisEquality,
isectElimination,
extract_by_obid,
introduction,
cut,
productEquality,
thin,
productElimination,
sqequalHypSubstitution,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
independent_pairFormation,
independent_functionElimination,
dependent_functionElimination
Latex:
\mforall{}e:BasicGeometry. \mforall{}a,b,c,d,e1,f,z:Point. ((((a=z=d \mwedge{} b=z=e1) \mwedge{} c=z=f) \mwedge{} a=b=c) {}\mRightarrow{} d=e1=f)
Date html generated:
2017_10_02-PM-06_33_52
Last ObjectModification:
2017_08_05-PM-04_44_05
Theory : euclidean!plane!geometry
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