Nuprl Lemma : eu-seg-length-test2
∀e:EuclideanPlane. ∀s1,s2:ProperSegment. ∀t1,t2,t3:Segment. (s1 ≡ s2 ⇒ t1 ≡ t2 ⇒ t2 ≡ t3 ⇒ s1 + t1 ≡ s2 + t3)
Proof
Definitions occuring in Statement :
eu-seg-extend: s + t,
eu-seg-congruent: s1 ≡ s2,
eu-proper-segment: ProperSegment,
eu-segment: Segment,
euclidean-plane: EuclideanPlane,
all: ∀x:A. B[x],
implies: P ⇒ Q
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
uiff: uiff(P;Q),
and: P ∧ Q,
prop: ℙ,
euclidean-plane: EuclideanPlane,
eu-proper-segment: ProperSegment
Lemmas referenced :
eu-seg-extend_functionality,
eu-seg-congruent-iff-length,
eu-seg-congruent_wf,
eu-segment_wf,
eu-proper-segment_wf,
euclidean-plane_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
isectElimination,
independent_isectElimination,
hypothesis,
because_Cache,
productElimination,
equalityTransitivity,
setElimination,
rename
Latex:
\mforall{}e:EuclideanPlane. \mforall{}s1,s2:ProperSegment. \mforall{}t1,t2,t3:Segment.
(s1 \mequiv{} s2 {}\mRightarrow{} t1 \mequiv{} t2 {}\mRightarrow{} t2 \mequiv{} t3 {}\mRightarrow{} s1 + t1 \mequiv{} s2 + t3)
Date html generated:
2016_05_18-AM-06_41_21
Last ObjectModification:
2015_12_28-AM-09_23_18
Theory : euclidean!geometry
Home
Index