Nuprl Lemma : qle-qabs
∀[q:ℚ]. (q ≤ |q|)
Proof
Definitions occuring in Statement : 
qabs: |r|
, 
qle: r ≤ s
, 
rationals: ℚ
, 
uall: ∀[x:A]. B[x]
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
implies: P 
⇒ Q
, 
true: True
, 
subtype_rel: A ⊆r B
, 
or: P ∨ Q
, 
uimplies: b supposing a
, 
prop: ℙ
, 
squash: ↓T
, 
guard: {T}
, 
iff: P 
⇐⇒ Q
, 
and: P ∧ Q
, 
rev_implies: P 
⇐ Q
, 
all: ∀x:A. B[x]
Lemmas referenced : 
qmax_ub, 
iff_weakening_equal, 
qabs-as-qmax, 
true_wf, 
squash_wf, 
qle_wf, 
qle_weakening_eq_qorder, 
int-subtype-rationals, 
qmul_wf, 
rationals_wf, 
qabs_wf, 
qle_witness
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation, 
introduction, 
cut, 
lemma_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
hypothesisEquality, 
hypothesis, 
independent_functionElimination, 
because_Cache, 
natural_numberEquality, 
minusEquality, 
applyEquality, 
sqequalRule, 
inlFormation, 
independent_isectElimination, 
lambdaEquality, 
imageElimination, 
equalityTransitivity, 
equalitySymmetry, 
imageMemberEquality, 
baseClosed, 
universeEquality, 
productElimination, 
dependent_functionElimination
Latex:
\mforall{}[q:\mBbbQ{}].  (q  \mleq{}  |q|)
Date html generated:
2016_05_15-PM-11_03_08
Last ObjectModification:
2016_01_16-PM-09_29_10
Theory : rationals
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