Nuprl Lemma : req_transitivity

[a,b,c:ℝ].  (a c) supposing ((b c) and (a b))


Definitions occuring in Statement :  req: y real: uimplies: supposing a uall: [x:A]. B[x]
Definitions unfolded in proof :  equiv_rel: EquivRel(T;x,y.E[x; y]) and: P ∧ Q uall: [x:A]. B[x] member: t ∈ T uimplies: supposing a implies:  Q prop: guard: {T} trans: Trans(T;x,y.E[x; y]) all: x:A. B[x]
Lemmas referenced :  req-equiv req_witness req_wf real_wf
Rules used in proof :  cut lemma_by_obid sqequalHypSubstitution sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity productElimination thin isect_memberFormation introduction isectElimination hypothesisEquality independent_functionElimination hypothesis sqequalRule isect_memberEquality because_Cache equalityTransitivity equalitySymmetry dependent_functionElimination

\mforall{}[a,b,c:\mBbbR{}].    (a  =  c)  supposing  ((b  =  c)  and  (a  =  b))

Date html generated: 2016_05_18-AM-06_50_33
Last ObjectModification: 2015_12_28-AM-00_29_02

Theory : reals

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