Nuprl Lemma : req-iff-rsub-is-0
∀[a,b:ℝ]. uiff(a = b;(a - b) = r0)
Proof
Definitions occuring in Statement :
rsub: x - y,
req: x = y,
int-to-real: r(n),
real: ℝ,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
natural_number: $n
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
implies: P ⇒ Q,
prop: ℙ,
rev_uimplies: rev_uimplies(P;Q),
rsub: x - y
Lemmas referenced :
req_witness,
rsub_wf,
int-to-real_wf,
req_wf,
real_wf,
radd-preserves-req,
radd_wf,
rminus_wf,
uiff_transitivity,
req_functionality,
radd-ac,
radd_comm,
radd_functionality,
radd-rminus-both,
req_weakening,
radd-zero-both
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
independent_pairFormation,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
natural_numberEquality,
independent_functionElimination,
sqequalRule,
productElimination,
independent_pairEquality,
isect_memberEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
independent_isectElimination
Latex:
\mforall{}[a,b:\mBbbR{}]. uiff(a = b;(a - b) = r0)
Date html generated:
2017_10_02-PM-07_20_44
Last ObjectModification:
2017_07_28-AM-07_21_39
Theory : reals
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