### Nuprl Lemma : rmul_functionality

`∀[r1,r2,s1,s2:ℝ].  ((r1 * s1) = (r2 * s2)) supposing ((s1 = s2) and (r1 = r2))`

Proof

Definitions occuring in Statement :  req: `x = y` rmul: `a * b` real: `ℝ` uimplies: `b supposing a` uall: `∀[x:A]. B[x]`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` uimplies: `b supposing a` uiff: `uiff(P;Q)` and: `P ∧ Q` all: `∀x:A. B[x]` subtype_rel: `A ⊆r B` real: `ℝ` implies: `P `` Q` iff: `P `⇐⇒` Q` rev_implies: `P `` Q` prop: `ℙ`
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

Latex:
\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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