### Nuprl Lemma : rmul-rdiv-cancel5

`∀[a,b,c:ℝ].  ((b/a) * (a/c)) = (b/c) supposing a ≠ r0 ∧ c ≠ r0`

Proof

Definitions occuring in Statement :  rdiv: `(x/y)` rneq: `x ≠ y` req: `x = y` rmul: `a * b` int-to-real: `r(n)` real: `ℝ` uimplies: `b 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: `b supposing a` and: `P ∧ Q` false: `False` implies: `P `` 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` pi2: `snd(t)` prop: `ℙ`
Lemmas referenced :  assert-rat-term-eq2 rtermMultiply_wf rtermDivide_wf rtermVar_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 sqequalHypSubstitution productElimination thin extract_by_obid isectElimination natural_numberEquality hypothesis lambdaEquality_alt int_eqEquality hypothesisEquality independent_isectElimination approximateComputation sqequalRule independent_pairFormation independent_functionElimination productIsType universeIsType isect_memberEquality_alt because_Cache isectIsTypeImplies inhabitedIsType

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

Date html generated: 2019_10_29-AM-09_55_12
Last ObjectModification: 2019_04_01-PM-07_05_36

Theory : reals

Home Index