Nuprl Lemma : geo-midpoint-diagonals-congruent2
∀e:BasicGeometry. ∀P,Q,R,S,P',Q',R',S',A:Point. (((((P=A=P' ∧ Q=A=Q') ∧ R=A=R') ∧ S=A=S') ∧ PQ ≅ RS) ⇒ P'Q' ≅ R'S')
Proof
Definitions occuring in Statement :
geo-midpoint: a=m=b,
basic-geometry: BasicGeometry,
geo-congruent: ab ≅ cd,
geo-point: Point,
all: ∀x:A. B[x],
implies: P ⇒ Q,
and: P ∧ Q
Definitions unfolded in proof :
uimplies: b supposing a,
guard: {T},
cand: A c∧ B,
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],
uiff: uiff(P;Q)
Lemmas referenced :
geo-point_wf,
Error :basic-geo-primitives_wf,
Error :basic-geo-structure_wf,
basic-geometry_wf,
subtype_rel_transitivity,
basic-geometry-subtype,
geo-congruent_wf,
geo-midpoint_wf,
geo-midpoint-diagonals-congruent,
geo-congruent-iff-length
Rules used in proof :
sqequalRule,
independent_isectElimination,
instantiate,
applyEquality,
because_Cache,
hypothesis,
hypothesisEquality,
isectElimination,
extract_by_obid,
introduction,
cut,
productEquality,
thin,
productElimination,
sqequalHypSubstitution,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
independent_functionElimination,
dependent_functionElimination,
equalitySymmetry,
equalityTransitivity
Latex:
\mforall{}e:BasicGeometry. \mforall{}P,Q,R,S,P',Q',R',S',A:Point.
(((((P=A=P' \mwedge{} Q=A=Q') \mwedge{} R=A=R') \mwedge{} S=A=S') \mwedge{} PQ \00D0 RS) {}\mRightarrow{} P'Q' \00D0 R'S')
Date html generated:
2017_10_02-PM-06_33_34
Last ObjectModification:
2017_08_05-PM-04_43_49
Theory : euclidean!plane!geometry
Home
Index