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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