Nuprl Lemma : rmul-rsub-distrib
∀[a,b,c:ℝ]. (((a * (b - c)) = ((a * b) - a * c)) ∧ (((b - c) * a) = ((b * a) - c * a)))
Proof
Definitions occuring in Statement :
rsub: x - y,
req: x = y,
rmul: 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,
uimplies: b supposing a,
rsub: x - y,
uiff: uiff(P;Q),
rev_uimplies: rev_uimplies(P;Q)
Lemmas referenced :
req_witness,
rmul_wf,
rsub_wf,
real_wf,
radd_wf,
rminus_wf,
req_weakening,
req_wf,
req_functionality,
req_transitivity,
rmul-distrib,
radd_functionality,
rmul_over_rminus,
uiff_transitivity,
rminus_functionality,
rmul_comm
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
independent_pairFormation,
hypothesis,
sqequalRule,
sqequalHypSubstitution,
productElimination,
thin,
independent_pairEquality,
extract_by_obid,
isectElimination,
hypothesisEquality,
independent_functionElimination,
isect_memberEquality,
because_Cache,
independent_isectElimination
Latex:
\mforall{}[a,b,c:\mBbbR{}]. (((a * (b - c)) = ((a * b) - a * c)) \mwedge{} (((b - c) * a) = ((b * a) - c * a)))
Date html generated:
2017_10_02-PM-07_17_35
Last ObjectModification:
2017_07_28-AM-07_21_12
Theory : reals
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