Nuprl Lemma : decidable__qle
∀a,b:ℚ. Dec(a ≤ b)
Proof
Definitions occuring in Statement :
qle: r ≤ s,
rationals: ℚ,
decidable: Dec(P),
all: ∀x:A. B[x]
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
qle: r ≤ s,
grp_leq: a ≤ b,
qadd_grp: <ℚ+>,
grp_le: ≤b,
pi2: snd(t),
pi1: fst(t),
infix_ap: x f y,
q_le: q_le(r;s),
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
callbyvalueall: callbyvalueall,
has-value: (a)↓,
has-valueall: has-valueall(a)
Lemmas referenced :
valueall-type-has-valueall,
rationals_wf,
rationals-valueall-type,
evalall-reduce,
member-decide-assert,
bor_wf,
qpositive_wf,
qsub_wf,
qeq_wf2
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
introduction,
sqequalRule,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
independent_isectElimination,
hypothesisEquality,
callbyvalueReduce,
because_Cache
Latex:
\mforall{}a,b:\mBbbQ{}. Dec(a \mleq{} b)
Date html generated:
2016_05_15-PM-10_55_34
Last ObjectModification:
2015_12_27-PM-07_52_35
Theory : rationals
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