Nuprl Lemma : assert-q_less
∀[a,b:ℚ]. (↑q_less(a;b) ~ a < b)
Proof
Definitions occuring in Statement :
q_less: q_less(r;s),
qless: r < s,
rationals: ℚ,
assert: ↑b,
uall: ∀[x:A]. B[x],
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
q_less: q_less(r;s),
qless: r < s,
grp_lt: a < b,
set_lt: a <p b
Lemmas referenced :
rational_set_blt,
rationals_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
sqequalAxiom,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[a,b:\mBbbQ{}]. (\muparrow{}q\_less(a;b) \msim{} a < b)
Date html generated:
2016_05_15-PM-10_57_25
Last ObjectModification:
2015_12_27-PM-07_52_07
Theory : rationals
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