Nuprl Lemma : rmul-distrib
∀[a,b,c:ℝ]. (((a * (b + c)) = ((a * b) + (a * c))) ∧ (((b + c) * a) = ((b * a) + (c * a))))
Proof
Definitions occuring in Statement :
req: x = y,
rmul: a * b,
radd: a + b,
real: ℝ,
uall: ∀[x:A]. B[x],
and: P ∧ Q
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
and: P ∧ Q,
cand: A c∧ B,
implies: P ⇒ Q
Lemmas referenced :
rmul-distrib1,
rmul-distrib2,
req_witness,
rmul_wf,
radd_wf,
real_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
independent_pairFormation,
because_Cache,
sqequalRule,
productElimination,
independent_pairEquality,
independent_functionElimination,
isect_memberEquality
Latex:
\mforall{}[a,b,c:\mBbbR{}]. (((a * (b + c)) = ((a * b) + (a * c))) \mwedge{} (((b + c) * a) = ((b * a) + (c * a))))
Date html generated:
2016_05_18-AM-06_52_30
Last ObjectModification:
2015_12_28-AM-00_30_44
Theory : reals
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