Nuprl Lemma : eu-five-segment
∀e:EuclideanPlane
∀[a,b,c,d,A,B,C,D:Point].
(cd=CD) supposing (bd=BD and ad=AD and bc=BC and ab=AB and A_B_C and a_b_c and (¬(a = b ∈ Point)))
Proof
Definitions occuring in Statement :
euclidean-plane: EuclideanPlane,
eu-between-eq: a_b_c,
eu-congruent: ab=cd,
eu-point: Point,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
not: ¬A,
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
euclidean-plane: EuclideanPlane,
member: t ∈ T,
uall: ∀[x:A]. B[x],
so_lambda: λ2x.t[x],
uimplies: b supposing a,
prop: ℙ,
so_apply: x[s],
euclidean-axioms: euclidean-axioms(e),
and: P ∧ Q,
cand: A c∧ B,
implies: P ⇒ Q,
not: ¬A,
false: False,
sq_stable: SqStable(P),
squash: ↓T
Lemmas referenced :
sq_stable__eu-congruent,
sq_stable__uall,
eu-congruent_wf,
eu-between-eq_wf,
equal_wf,
not_wf,
isect_wf,
uall_wf,
eu-point_wf,
euclidean-plane_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
sqequalHypSubstitution,
setElimination,
thin,
rename,
cut,
lemma_by_obid,
hypothesis,
isectElimination,
hypothesisEquality,
lambdaEquality,
sqequalRule,
because_Cache,
equalityEquality,
productElimination,
independent_functionElimination,
isect_memberFormation,
introduction,
dependent_functionElimination,
voidElimination,
imageMemberEquality,
baseClosed,
imageElimination
Latex:
\mforall{}e:EuclideanPlane
\mforall{}[a,b,c,d,A,B,C,D:Point].
(cd=CD) supposing (bd=BD and ad=AD and bc=BC and ab=AB and A\_B\_C and a\_b\_c and (\mneg{}(a = b)))
Date html generated:
2016_05_18-AM-06_35_15
Last ObjectModification:
2016_01_16-PM-10_31_29
Theory : euclidean!geometry
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