Nuprl Lemma : geo-perp-in-unicity1
∀e:BasicGeometry. ∀x,a,b,c:Point. (ba ⊥x ca ⇒ x ≡ a)
Proof
Definitions occuring in Statement :
geo-perp-in: ab ⊥x cd,
basic-geometry: BasicGeometry,
geo-eq: a ≡ b,
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,
and: P ∧ Q,
geo-perp-in: ab ⊥x cd,
implies: P ⇒ Q,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q
Lemmas referenced :
geo-colinear-same,
Error :basic-geo-primitives_wf,
Error :basic-geo-structure_wf,
basic-geometry_wf,
subtype_rel_transitivity,
basic-geometry-subtype,
geo-point_wf,
geo-perp-in_wf,
geo-eq_weakening,
right-angle_functionality,
right-angle-legs-same,
right-angle_wf
Rules used in proof :
independent_functionElimination,
dependent_functionElimination,
because_Cache,
sqequalRule,
independent_isectElimination,
instantiate,
applyEquality,
hypothesis,
hypothesisEquality,
isectElimination,
extract_by_obid,
introduction,
cut,
thin,
productElimination,
sqequalHypSubstitution,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
impliesLevelFunctionality,
allLevelFunctionality,
levelHypothesis,
impliesFunctionality,
allFunctionality,
addLevel,
promote_hyp
Latex:
\mforall{}e:BasicGeometry. \mforall{}x,a,b,c:Point. (ba \mbot{}x ca {}\mRightarrow{} x \mequiv{} a)
Date html generated:
2017_10_02-PM-06_43_22
Last ObjectModification:
2017_08_05-PM-04_49_20
Theory : euclidean!plane!geometry
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