Nuprl Lemma : assert-q_le-eq
∀[a,b:ℚ]. ((↑q_le(a;b)) = (a ≤ b) ∈ ℙ)
Proof
Definitions occuring in Statement :
qle: r ≤ s,
q_le: q_le(r;s),
rationals: ℚ,
assert: ↑b,
uall: ∀[x:A]. B[x],
prop: ℙ,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T
Lemmas referenced :
assert-q_le,
qle_wf,
rationals_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
isect_memberEquality,
axiomEquality,
because_Cache
Latex:
\mforall{}[a,b:\mBbbQ{}]. ((\muparrow{}q\_le(a;b)) = (a \mleq{} b))
Date html generated:
2016_05_15-PM-10_57_36
Last ObjectModification:
2015_12_27-PM-07_51_43
Theory : rationals
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