Nuprl Lemma : rmul-one-both
∀[x:ℝ]. (((x * r1) = x) ∧ ((r1 * x) = x))
Proof
Definitions occuring in Statement :
req: x = y,
rmul: a * b,
int-to-real: r(n),
real: ℝ,
uall: ∀[x:A]. B[x],
and: P ∧ Q,
natural_number: $n
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-one,
rmul-identity1,
req_witness,
rmul_wf,
int-to-real_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,
natural_numberEquality,
independent_functionElimination
Latex:
\mforall{}[x:\mBbbR{}]. (((x * r1) = x) \mwedge{} ((r1 * x) = x))
Date html generated:
2016_05_18-AM-06_52_14
Last ObjectModification:
2015_12_28-AM-00_30_20
Theory : reals
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