Nuprl Lemma : eu-five-segment

    (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)))


Definitions occuring in Statement :  euclidean-plane: EuclideanPlane eu-between-eq: a_b_c eu-congruent: ab=cd eu-point: Point uimplies: supposing a uall: [x:A]. B[x] all: x:A. B[x] not: ¬A equal: 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: supposing a prop: so_apply: x[s] euclidean-axioms: euclidean-axioms(e) and: P ∧ Q cand: c∧ B implies:  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

        (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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