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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