Nuprl Lemma : rmul-rdiv-cancel9

[a,b,c:ℝ].  (a b/c b) (a/c) supposing b ≠ r0 ∧ c ≠ 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] and: P ∧ Q natural_number: $n
Definitions unfolded in proof :  uall: [x:A]. B[x] member: t ∈ T uimplies: supposing a and: P ∧ Q 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 rtermVar: rtermVar(var) pi1: fst(t) true: True rtermMultiply: left "*" right all: x:A. B[x] pi2: snd(t) prop:
Lemmas referenced :  assert-rat-term-eq2 rtermDivide_wf rtermMultiply_wf rtermVar_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 sqequalHypSubstitution productElimination thin extract_by_obid isectElimination natural_numberEquality hypothesis lambdaEquality_alt int_eqEquality hypothesisEquality independent_isectElimination approximateComputation sqequalRule independent_pairFormation dependent_functionElimination independent_functionElimination because_Cache productIsType universeIsType isect_memberEquality_alt isectIsTypeImplies inhabitedIsType

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



Date html generated: 2019_10_29-AM-09_55_52
Last ObjectModification: 2019_04_01-PM-07_07_16

Theory : reals


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