Nuprl Lemma : implies-right-angle
∀e:BasicGeometry. ∀a,b,c,c':Point. (c'=b=c ⇒ ac ≅ ac' ⇒ Rabc)
Proof
Definitions occuring in Statement :
right-angle: Rabc,
geo-midpoint: a=m=b,
basic-geometry: BasicGeometry,
geo-congruent: ab ≅ cd,
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],
and: P ∧ Q,
iff: 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-eq_weakening,
geo-congruent_functionality,
symmetric-point-unicity2
Rules used in proof :
sqequalRule,
independent_isectElimination,
instantiate,
applyEquality,
because_Cache,
hypothesis,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
introduction,
cut,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
productElimination,
promote_hyp,
independent_functionElimination,
dependent_functionElimination
Latex:
\mforall{}e:BasicGeometry. \mforall{}a,b,c,c':Point. (c'=b=c {}\mRightarrow{} ac \00D0 ac' {}\mRightarrow{} Rabc)
Date html generated:
2017_10_02-PM-06_40_42
Last ObjectModification:
2017_08_05-PM-04_47_17
Theory : euclidean!plane!geometry
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