Nuprl Lemma : geo-fsc-ap
∀e:BasicGeometry. ∀a,b,c,d,a',b',c',d':Point. (FSC(a;b;c;d a';b';c';d') ⇒ a ≠ b ⇒ cd ≅ c'd')
Proof
Definitions occuring in Statement :
geo-five-seg-compressed: FSC(a;b;c;d a';b';c';d'),
basic-geometry: BasicGeometry,
geo-congruent: ab ≅ cd,
geo-sep: 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,
implies: P ⇒ Q,
all: ∀x:A. B[x],
geo-five-seg-compressed: FSC(a;b;c;d a';b';c';d'),
geo-cong-tri: Cong3(abc,a'b'c'),
and: P ∧ Q,
uiff: uiff(P;Q)
Lemmas referenced :
geo-point_wf,
geo-five-seg-compressed_wf,
Error :basic-geo-primitives_wf,
Error :basic-geo-structure_wf,
basic-geometry_wf,
subtype_rel_transitivity,
basic-geometry-subtype,
geo-sep_wf,
geo-colinear-five-segment,
geo-length-flip,
geo-congruent-iff-length
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,
productElimination,
dependent_functionElimination,
equalitySymmetry,
equalityTransitivity
Latex:
\mforall{}e:BasicGeometry. \mforall{}a,b,c,d,a',b',c',d':Point. (FSC(a;b;c;d a';b';c';d') {}\mRightarrow{} a \mneq{} b {}\mRightarrow{} cd \00D0 c'd')
Date html generated:
2017_10_02-PM-06_31_42
Last ObjectModification:
2017_08_05-PM-04_42_41
Theory : euclidean!plane!geometry
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