Nuprl Lemma : req_transitivity

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

Proof

Definitions occuring in Statement :  req: `x = y` real: `ℝ` uimplies: `b 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: `b supposing a` implies: `P `` Q` prop: `ℙ` 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

Latex:
\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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