Nuprl Lemma : out-cong-angle
∀e:BasicGeometry. ∀a,b,c,a',c':Point. (out(b cc') ⇒ out(b aa') ⇒ abc ≅a a'bc')
Proof
Definitions occuring in Statement :
geo-out: out(p ab),
geo-cong-angle: abc ≅a xyz,
basic-geometry: BasicGeometry,
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,
and: P ∧ Q,
cand: A c∧ B,
basic-geometry: BasicGeometry,
geo-out: out(p ab)
Lemmas referenced :
geo-out_wf,
geo-point_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-cong-angle-refl,
geo-sep-sym,
geo-out_weakening,
geo-eq_weakening,
out-preserves-angle-cong_1
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
applyEquality,
instantiate,
independent_isectElimination,
sqequalRule,
because_Cache,
dependent_functionElimination,
independent_functionElimination,
productElimination,
independent_pairFormation
Latex:
\mforall{}e:BasicGeometry. \mforall{}a,b,c,a',c':Point. (out(b cc') {}\mRightarrow{} out(b aa') {}\mRightarrow{} abc \00D0\msuba{} a'bc')
Date html generated:
2017_10_02-PM-06_30_22
Last ObjectModification:
2017_08_17-PM-06_16_30
Theory : euclidean!plane!geometry
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