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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