Nuprl Lemma : assert-q_less-eq
∀[a,b:ℚ]. ((↑q_less(a;b)) = a < b ∈ ℙ)
Proof
Definitions occuring in Statement :
q_less: q_less(r;s),
qless: 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_less,
qless_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\_less(a;b)) = a < b)
Date html generated:
2016_05_15-PM-10_57_29
Last ObjectModification:
2015_12_27-PM-07_52_02
Theory : rationals
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