Nuprl Lemma : right-angle-symmetry
∀e:BasicGeometry. ∀a,b,c:Point. (Rabc ⇒ Rcba)
Proof
Definitions occuring in Statement :
right-angle: Rabc,
basic-geometry: BasicGeometry,
geo-point: Point,
all: ∀x:A. B[x],
implies: 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,
right-angle: Rabc,
implies: P ⇒ Q,
all: ∀x:A. B[x],
rev_implies: P ⇐ Q,
and: P ∧ Q,
iff: P ⇐⇒ Q,
geo-eq: a ≡ b,
false: False,
exists: ∃x:A. B[x],
or: P ∨ Q,
not: ¬A,
stable: Stable{P},
basic-geometry: BasicGeometry,
uiff: uiff(P;Q),
geo-midpoint: a=m=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,
right-angle_wf,
geo-midpoint_wf,
minimal-not-not-excluded-middle,
geo-eq_weakening,
geo-congruent_functionality,
geo-sep-sym,
symmetric-point-construction,
geo-congruent_wf,
not_wf,
geo-sep_wf,
or_wf,
false_wf,
minimal-double-negation-hyp-elim,
stable__geo-congruent,
geo-midpoint-symmetry,
geo-length-flip,
geo-congruent-iff-length,
symmetry-preserves-congruence
Rules used in proof :
sqequalRule,
independent_isectElimination,
instantiate,
applyEquality,
because_Cache,
hypothesis,
hypothesisEquality,
thin,
isectElimination,
extract_by_obid,
introduction,
cut,
rename,
sqequalHypSubstitution,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
voidElimination,
productElimination,
unionElimination,
independent_functionElimination,
functionEquality,
setElimination,
dependent_functionElimination,
equalitySymmetry,
equalityTransitivity
Latex:
\mforall{}e:BasicGeometry. \mforall{}a,b,c:Point. (Rabc {}\mRightarrow{} Rcba)
Date html generated:
2017_10_02-PM-06_40_49
Last ObjectModification:
2017_08_05-PM-04_47_23
Theory : euclidean!plane!geometry
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