Nuprl Lemma : hp-cong-angle-reflexive
∀e:EuclideanPlane. ∀a,b,c:Point. (a leftof bc ⇒ abc ≅ρ abc)
Proof
Definitions occuring in Statement :
half-plane-cong-angle: abc ≅ρ dbc,
euclidean-plane: EuclideanPlane,
geo-left: a leftof bc,
geo-point: Point,
all: ∀x:A. B[x],
implies: P ⇒ Q
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
half-plane-cong-angle: abc ≅ρ dbc,
and: P ∧ Q,
cand: A c∧ B,
uall: ∀[x:A]. B[x],
member: t ∈ T,
basic-geometry: BasicGeometry,
prop: ℙ,
subtype_rel: A ⊆r B,
guard: {T},
uimplies: b supposing a
Lemmas referenced :
geo-colinear-same,
geo-left_wf,
euclidean-plane-structure-subtype,
euclidean-plane-subtype,
subtype_rel_transitivity,
euclidean-plane_wf,
euclidean-plane-structure_wf,
geo-primitives_wf,
geo-point_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
independent_pairFormation,
cut,
hypothesis,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
sqequalRule,
hypothesisEquality,
productElimination,
applyEquality,
instantiate,
independent_isectElimination,
because_Cache
Latex:
\mforall{}e:EuclideanPlane. \mforall{}a,b,c:Point. (a leftof bc {}\mRightarrow{} abc \00D0\mrho{} abc)
Date html generated:
2017_10_02-PM-04_48_58
Last ObjectModification:
2017_08_24-PM-03_37_58
Theory : euclidean!plane!geometry
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