Nuprl Lemma : eu-inner-five-segment

`∀e:EuclideanPlane`
`  ∀[a,b,c,d,A,B,C,D:Point].  (bd=BD) supposing (cd=CD and ad=AD and bc=BC and ac=AC and A_B_C and a_b_c)`

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]`
Definitions unfolded in proof :  all: `∀x:A. B[x]` uall: `∀[x:A]. B[x]` uimplies: `b supposing a` member: `t ∈ T` euclidean-plane: `EuclideanPlane` sq_stable: `SqStable(P)` implies: `P `` Q` stable: `Stable{P}` not: `¬A` prop: `ℙ` squash: `↓T` guard: `{T}` and: `P ∧ Q` false: `False` exists: `∃x:A. B[x]` cand: `A c∧ B` uiff: `uiff(P;Q)`
Lemmas referenced :  sq_stable__eu-congruent stable__eu-congruent not_wf eu-congruent_wf eu-between-eq_wf eu-point_wf euclidean-plane_wf eu-between-eq-same eu-congruence-identity-sym equal_wf and_wf false_wf eu-extend-exists eu-congruence-identity eu-five-segment eu-congruent-iff-length eu-between-eq-symmetry eu-between-eq-inner-trans eu-length-flip
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity lambdaFormation isect_memberFormation cut introduction extract_by_obid sqequalHypSubstitution dependent_functionElimination thin setElimination rename because_Cache hypothesis isectElimination hypothesisEquality independent_functionElimination independent_isectElimination sqequalRule imageMemberEquality baseClosed imageElimination promote_hyp equalitySymmetry hyp_replacement Error :applyLambdaEquality,  dependent_set_memberEquality independent_pairFormation applyEquality lambdaEquality productElimination setEquality voidElimination dependent_pairFormation equalityTransitivity equalityEquality universeEquality productEquality

Latex:
\mforall{}e:EuclideanPlane
\mforall{}[a,b,c,d,A,B,C,D:Point].
(bd=BD)  supposing  (cd=CD  and  ad=AD  and  bc=BC  and  ac=AC  and  A\_B\_C  and  a\_b\_c)

Date html generated: 2016_10_26-AM-07_42_21
Last ObjectModification: 2016_07_12-AM-08_08_46

Theory : euclidean!geometry

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