Nuprl Lemma : right-angle_functionality
∀e:BasicGeometry. ∀a,b,c,a',b',c':Point. (a ≡ a' ⇒ b ≡ b' ⇒ c ≡ c' ⇒ {Rabc ⇐⇒ Ra'b'c'})
Proof
Definitions occuring in Statement :
right-angle: Rabc,
basic-geometry: BasicGeometry,
geo-eq: a ≡ b,
geo-point: Point,
guard: {T},
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
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,
implies: P ⇒ Q,
all: ∀x:A. B[x],
rev_implies: P ⇐ Q,
right-angle: Rabc,
and: P ∧ Q,
iff: P ⇐⇒ Q,
so_apply: x[s],
so_lambda: λ2x.t[x]
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-eq_wf,
right-angle_wf,
geo-congruent_functionality,
geo-eq_weakening,
geo-eq_inversion,
geo-midpoint_functionality,
implies_functionality_wrt_implies,
all_functionality_wrt_implies,
geo-congruent_wf,
geo-midpoint_wf
Rules used in proof :
because_Cache,
sqequalRule,
independent_isectElimination,
instantiate,
hypothesis,
applyEquality,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
introduction,
cut,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
independent_pairFormation,
productElimination,
dependent_functionElimination,
independent_functionElimination,
equalitySymmetry,
equalityTransitivity,
functionEquality,
lambdaEquality
Latex:
\mforall{}e:BasicGeometry. \mforall{}a,b,c,a',b',c':Point. (a \mequiv{} a' {}\mRightarrow{} b \mequiv{} b' {}\mRightarrow{} c \mequiv{} c' {}\mRightarrow{} \{Rabc \mLeftarrow{}{}\mRightarrow{} Ra'b'c'\})
Date html generated:
2017_10_02-PM-06_40_29
Last ObjectModification:
2017_08_05-PM-04_47_04
Theory : euclidean!plane!geometry
Home
Index