Nuprl Lemma : rmul-rdiv

[x,y,a,b:ℝ].  (((x/a) (y/b)) (x y/a b)) supposing (b ≠ r0 and a ≠ r0)


Definitions occuring in Statement :  rdiv: (x/y) rneq: x ≠ y req: y rmul: b int-to-real: r(n) real: uimplies: supposing a uall: [x:A]. B[x] natural_number: $n
Definitions unfolded in proof :  uall: [x:A]. B[x] member: t ∈ T uimplies: supposing a false: False implies:  Q not: ¬A rat_term_to_real: rat_term_to_real(f;t) rtermDivide: num "/" denom rat_term_ind: rat_term_ind rtermMultiply: left "*" right rtermVar: rtermVar(var) pi1: fst(t) and: P ∧ Q true: True all: x:A. B[x] pi2: snd(t) prop:
Lemmas referenced :  assert-rat-term-eq2 rtermMultiply_wf rtermDivide_wf rtermVar_wf int-to-real_wf istype-int rmul-neq-zero req_witness rmul_wf rdiv_wf rneq_wf real_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation_alt introduction cut extract_by_obid sqequalHypSubstitution isectElimination thin natural_numberEquality hypothesis lambdaEquality_alt int_eqEquality hypothesisEquality independent_isectElimination approximateComputation sqequalRule independent_pairFormation dependent_functionElimination independent_functionElimination because_Cache universeIsType isect_memberEquality_alt isectIsTypeImplies inhabitedIsType

\mforall{}[x,y,a,b:\mBbbR{}].    (((x/a)  *  (y/b))  =  (x  *  y/a  *  b))  supposing  (b  \mneq{}  r0  and  a  \mneq{}  r0)

Date html generated: 2019_10_29-AM-09_56_49
Last ObjectModification: 2019_04_01-PM-07_09_13

Theory : reals

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