Nuprl Lemma : rmul-zero-both
∀[x:ℝ]. (((x * r0) = r0) ∧ ((r0 * x) = r0))
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,
uimplies: b supposing a,
uiff: uiff(P;Q),
rev_uimplies: rev_uimplies(P;Q)
Lemmas referenced :
rmul-zero,
req_witness,
rmul_wf,
int-to-real_wf,
real_wf,
req_functionality,
rmul_comm,
req_weakening
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
independent_pairFormation,
sqequalRule,
productElimination,
independent_pairEquality,
natural_numberEquality,
independent_functionElimination,
because_Cache,
independent_isectElimination
Latex:
\mforall{}[x:\mBbbR{}]. (((x * r0) = r0) \mwedge{} ((r0 * x) = r0))
Date html generated:
2016_05_18-AM-06_52_05
Last ObjectModification:
2015_12_28-AM-00_30_25
Theory : reals
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