Nuprl Lemma : q-ceil-property
∀[r:ℚ]. (q-ceil(r) - 1 < r ∧ (r ≤ q-ceil(r)))
Proof
Definitions occuring in Statement :
q-ceil: q-ceil(r),
qle: r ≤ s,
qless: r < s,
qsub: r - s,
rationals: ℚ,
uall: ∀[x:A]. B[x],
and: P ∧ Q,
natural_number: $n
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
q-ceil: q-ceil(r),
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
and: P ∧ Q,
prop: ℙ,
so_apply: x[s],
all: ∀x:A. B[x],
implies: P ⇒ Q,
cand: A c∧ B,
sq_stable: SqStable(P),
squash: ↓T
Lemmas referenced :
decidable__qle,
decidable__qless,
sq_stable_from_decidable,
sq_stable__and,
qsub-sub,
squash_wf,
rationals_wf,
qle_witness,
q-ceil_wf,
qsub_wf,
qless_witness,
equal_wf,
qle_wf,
int-subtype-rationals,
subtract_wf,
qless_wf,
and_wf,
set_wf,
rat-int-bound_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
intEquality,
sqequalRule,
lambdaEquality,
natural_numberEquality,
applyEquality,
because_Cache,
lambdaFormation,
setElimination,
rename,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
independent_functionElimination,
productElimination,
independent_pairEquality,
isect_memberEquality,
independent_pairFormation,
imageMemberEquality,
baseClosed,
imageElimination
Latex:
\mforall{}[r:\mBbbQ{}]. (q-ceil(r) - 1 < r \mwedge{} (r \mleq{} q-ceil(r)))
Date html generated:
2016_05_15-PM-11_35_03
Last ObjectModification:
2016_01_16-PM-09_12_33
Theory : rationals
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