Nuprl Lemma : assert-q_le
∀[a,b:ℚ]. (↑q_le(a;b) ~ a ≤ b)
Proof
Definitions occuring in Statement :
qle: r ≤ s,
q_le: q_le(r;s),
rationals: ℚ,
assert: ↑b,
uall: ∀[x:A]. B[x],
sqequal: s ~ t
Definitions unfolded in proof :
qle: r ≤ s,
q_le: q_le(r;s),
grp_leq: a ≤ b,
qadd_grp: <ℚ+>,
grp_le: ≤b,
pi2: snd(t),
pi1: fst(t),
infix_ap: x f y,
uall: ∀[x:A]. B[x],
member: t ∈ T
Lemmas referenced :
rationals_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
sqequalAxiom,
lemma_by_obid,
hypothesis,
sqequalHypSubstitution,
isect_memberEquality,
isectElimination,
thin,
hypothesisEquality,
because_Cache
Latex:
\mforall{}[a,b:\mBbbQ{}]. (\muparrow{}q\_le(a;b) \msim{} a \mleq{} b)
Date html generated:
2016_05_15-PM-10_57_33
Last ObjectModification:
2015_12_27-PM-07_51_50
Theory : rationals
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