Nuprl Lemma : qround_wf
∀[r:ℚ]. ∀[k:ℕ+]. (qround(r;k) ∈ ℚ)
Proof
Definitions occuring in Statement :
qround: qround(r;k),
rationals: ℚ,
nat_plus: ℕ+,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
qround: qround(r;k),
nat_plus: ℕ+,
less_than: a < b,
squash: ↓T,
less_than': less_than'(a;b),
true: True,
and: P ∧ Q,
prop: ℙ,
int_nzero: ℤ-o,
nequal: a ≠ b ∈ T ,
not: ¬A,
implies: P ⇒ Q,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
all: ∀x:A. B[x],
top: Top
Lemmas referenced :
rationals_wf,
nat_plus_wf,
nequal_wf,
equal_wf,
int_formula_prop_wf,
int_formula_prop_less_lemma,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_term_value_mul_lemma,
int_formula_prop_eq_lemma,
int_formula_prop_and_lemma,
intformless_wf,
itermVar_wf,
itermConstant_wf,
itermMultiply_wf,
intformeq_wf,
intformand_wf,
satisfiable-full-omega-tt,
nat_plus_properties,
less_than_wf,
mul_nat_plus,
rounded-numerator_wf,
mk-rational_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
dependent_set_memberEquality,
natural_numberEquality,
independent_pairFormation,
imageMemberEquality,
baseClosed,
hypothesis,
multiplyEquality,
setElimination,
rename,
lambdaFormation,
independent_isectElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
computeAll,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
because_Cache
Latex:
\mforall{}[r:\mBbbQ{}]. \mforall{}[k:\mBbbN{}\msupplus{}]. (qround(r;k) \mmember{} \mBbbQ{})
Date html generated:
2016_05_15-PM-10_38_01
Last ObjectModification:
2016_01_16-PM-09_37_01
Theory : rationals
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