Nuprl Lemma : rmul_functionality

[r1,r2,s1,s2:ℝ].  ((r1 s1) (r2 s2)) supposing ((s1 s2) and (r1 r2))


Definitions occuring in Statement :  req: y rmul: b real: uimplies: supposing a uall: [x:A]. B[x]
Definitions unfolded in proof :  uall: [x:A]. B[x] member: t ∈ T uimplies: supposing a uiff: uiff(P;Q) and: P ∧ Q all: x:A. B[x] subtype_rel: A ⊆B real: implies:  Q iff: ⇐⇒ Q rev_implies:  Q prop:
Lemmas referenced :  req-iff-bdd-diff rmul_wf bdd-diff_functionality reg-seq-mul_wf rmul-bdd-diff-reg-seq-mul reg-seq-mul_functionality_wrt_bdd-diff req_witness req_wf real_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut lemma_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality hypothesis productElimination independent_isectElimination dependent_functionElimination applyEquality lambdaEquality setElimination rename because_Cache sqequalRule independent_functionElimination isect_memberEquality equalityTransitivity equalitySymmetry

\mforall{}[r1,r2,s1,s2:\mBbbR{}].    ((r1  *  s1)  =  (r2  *  s2))  supposing  ((s1  =  s2)  and  (r1  =  r2))

Date html generated: 2016_05_18-AM-06_51_33
Last ObjectModification: 2015_12_28-AM-00_29_51

Theory : reals

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