Nuprl Lemma : right-angle-colinear2
∀e:BasicGeometry. ∀a,b,c,c':Point. (Rabc ⇒ c ≠ b ⇒ Colinear(b;c;c') ⇒ Rabc')
Proof
Definitions occuring in Statement :
basic-geometry: BasicGeometry,
right-angle: Rabc,
geo-colinear: Colinear(a;b;c),
geo-sep: a ≠ b,
geo-point: Point,
all: ∀x:A. B[x],
implies: P ⇒ Q
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
prop: ℙ,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
guard: {T},
uimplies: b supposing a,
basic-geometry: BasicGeometry,
stable: Stable{P},
not: ¬A,
or: P ∨ Q,
false: False,
geo-eq: a ≡ b,
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
geo-colinear_wf,
euclidean-plane-structure-subtype,
euclidean-plane-subtype,
basic-geometry-subtype,
subtype_rel_transitivity,
basic-geometry_wf,
euclidean-plane_wf,
euclidean-plane-structure_wf,
geo-primitives_wf,
geo-sep_wf,
right-angle_wf,
geo-point_wf,
stable__not,
not_wf,
false_wf,
or_wf,
stable__right-angle,
minimal-double-negation-hyp-elim,
right-angle_functionality,
geo-eq_weakening,
minimal-not-not-excluded-middle,
right-angle-symmetry,
right-angle-colinear,
right-angle-trivial2
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
applyEquality,
hypothesis,
instantiate,
independent_isectElimination,
sqequalRule,
because_Cache,
functionEquality,
dependent_functionElimination,
independent_functionElimination,
unionElimination,
voidElimination,
productElimination
Latex:
\mforall{}e:BasicGeometry. \mforall{}a,b,c,c':Point. (Rabc {}\mRightarrow{} c \mneq{} b {}\mRightarrow{} Colinear(b;c;c') {}\mRightarrow{} Rabc')
Date html generated:
2018_05_22-PM-00_02_33
Last ObjectModification:
2018_04_19-PM-07_41_39
Theory : euclidean!plane!geometry
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