Nuprl Lemma : eu-fsc-ap
∀e:EuclideanPlane. ∀a,b,c,d,a',b',c',d':Point. (FSC(a;b;c;d a';b';c';d') ⇒ (¬(a = b ∈ Point)) ⇒ cd=c'd')
Proof
Definitions occuring in Statement :
eu-five-seg-compressed: FSC(a;b;c;d a';b';c';d'),
euclidean-plane: EuclideanPlane,
eu-congruent: ab=cd,
eu-point: Point,
all: ∀x:A. B[x],
not: ¬A,
implies: P ⇒ Q,
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
prop: ℙ,
uall: ∀[x:A]. B[x],
euclidean-plane: EuclideanPlane,
eu-five-seg-compressed: FSC(a;b;c;d a';b';c';d'),
uimplies: b supposing a,
and: P ∧ Q,
eu-cong-tri: Cong3(abc,a'b'c'),
uiff: uiff(P;Q)
Lemmas referenced :
not_wf,
equal_wf,
eu-point_wf,
eu-five-seg-compressed_wf,
euclidean-plane_wf,
eu-colinear-five-segment,
eu-congruent-iff-length,
eu-length-flip
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
setElimination,
rename,
hypothesisEquality,
hypothesis,
dependent_functionElimination,
independent_isectElimination,
productElimination,
because_Cache,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}e:EuclideanPlane. \mforall{}a,b,c,d,a',b',c',d':Point. (FSC(a;b;c;d a';b';c';d') {}\mRightarrow{} (\mneg{}(a = b)) {}\mRightarrow{} cd=c'd')
Date html generated:
2016_05_18-AM-06_42_14
Last ObjectModification:
2015_12_28-AM-09_22_42
Theory : euclidean!geometry
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