Nuprl Lemma : rmul-rdiv-cancel3

[a,b,c:ℝ].  (a (b/a) c) (b c) supposing a ≠ r0


Proof




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 rtermVar: rtermVar(var) pi1: fst(t) and: P ∧ Q true: True rtermDivide: num "/" denom pi2: snd(t) prop:
Lemmas referenced :  assert-rat-term-eq2 rtermMultiply_wf rtermVar_wf rtermDivide_wf int-to-real_wf istype-int 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 independent_functionElimination universeIsType isect_memberEquality_alt because_Cache isectIsTypeImplies inhabitedIsType

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



Date html generated: 2019_10_29-AM-09_54_51
Last ObjectModification: 2019_04_01-PM-07_04_34

Theory : reals


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