Nuprl Lemma : qabs_wf
∀[r:ℚ]. (|r| ∈ ℚ)
Proof
Definitions occuring in Statement :
qabs: |r|,
rationals: ℚ,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
qabs: |r|,
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
callbyvalueall: callbyvalueall,
has-value: (a)↓,
has-valueall: has-valueall(a),
subtype_rel: A ⊆r B
Lemmas referenced :
valueall-type-has-valueall,
rationals_wf,
rationals-valueall-type,
evalall-reduce,
ifthenelse_wf,
qpositive_wf,
qmul_wf,
int-subtype-rationals
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
independent_isectElimination,
hypothesisEquality,
callbyvalueReduce,
minusEquality,
natural_numberEquality,
applyEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[r:\mBbbQ{}]. (|r| \mmember{} \mBbbQ{})
Date html generated:
2016_05_15-PM-10_44_38
Last ObjectModification:
2015_12_27-PM-07_54_53
Theory : rationals
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