Nuprl Lemma : fractional-part_wf
∀q:ℚ. (fractional-part(q) ∈ {r:ℚ| (0 ≤ r) ∧ r < 1} )
Proof
Definitions occuring in Statement :
fractional-part: fractional-part(q),
qle: r ≤ s,
qless: r < s,
rationals: ℚ,
all: ∀x:A. B[x],
and: P ∧ Q,
member: t ∈ T,
set: {x:A| B[x]} ,
natural_number: $n
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
fractional-part: fractional-part(q),
uall: ∀[x:A]. B[x],
so_lambda: λ2x.t[x],
and: P ∧ Q,
pi1: fst(t),
pi2: snd(t),
subtype_rel: A ⊆r B,
prop: ℙ,
so_apply: x[s],
implies: P ⇒ Q
Lemmas referenced :
set_wf,
equal_wf,
qadd_wf,
int-subtype-rationals,
pi2_wf,
rationals_wf,
qle_wf,
qless_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
sqequalRule,
because_Cache,
thin,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
lambdaEquality,
productEquality,
productElimination,
hypothesisEquality,
applyEquality,
hypothesis,
setElimination,
rename,
dependent_set_memberEquality,
intEquality,
independent_pairEquality,
independent_pairFormation,
natural_numberEquality,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
independent_functionElimination
Latex:
\mforall{}q:\mBbbQ{}. (fractional-part(q) \mmember{} \{r:\mBbbQ{}| (0 \mleq{} r) \mwedge{} r < 1\} )
Date html generated:
2018_05_22-AM-00_30_50
Last ObjectModification:
2017_07_26-PM-06_58_39
Theory : rationals
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