Nuprl Lemma : rmul-rdiv2

[x,a,b:ℝ].  ((x/a b) ((x/a) (r1/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) rtermMultiply: left "*" right rat_term_ind: rat_term_ind rtermDivide: num "/" denom rtermConstant: "const" 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 rtermDivide_wf rtermVar_wf rtermMultiply_wf rtermConstant_wf int-to-real_wf istype-int rmul-neq-zero req_witness rdiv_wf rmul_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,a,b:\mBbbR{}].    ((x/a  *  b)  =  ((x/a)  *  (r1/b)))  supposing  (b  \mneq{}  r0  and  a  \mneq{}  r0)

Date html generated: 2019_10_29-AM-09_57_10
Last ObjectModification: 2019_04_01-PM-07_10_28

Theory : reals

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