Nuprl Lemma : q_le-elim
∀[r,s:ℚ]. (q_le(r;s) ~ qpositive(s + -(r)) ∨bqeq(r;s))
Proof
Definitions occuring in Statement :
q_le: q_le(r;s),
qpositive: qpositive(r),
qmul: r * s,
qadd: r + s,
rationals: ℚ,
qeq: qeq(r;s),
bor: p ∨bq,
uall: ∀[x:A]. B[x],
minus: -n,
natural_number: $n,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
q_le: q_le(r;s),
uimplies: b supposing a,
callbyvalueall: callbyvalueall,
has-value: (a)↓,
has-valueall: has-valueall(a),
qsub: r - s
Lemmas referenced :
valueall-type-has-valueall,
rationals_wf,
rationals-valueall-type,
evalall-reduce
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
independent_isectElimination,
hypothesisEquality,
callbyvalueReduce,
because_Cache,
sqequalAxiom,
isect_memberEquality
Latex:
\mforall{}[r,s:\mBbbQ{}]. (q\_le(r;s) \msim{} qpositive(s + -(r)) \mvee{}\msubb{}qeq(r;s))
Date html generated:
2016_05_15-PM-10_40_39
Last ObjectModification:
2015_12_27-PM-07_58_16
Theory : rationals
Home
Index