Nuprl Lemma : ratreal-req
∀[a:ℤ]. ∀[b:ℕ+]. (ratreal(<a, b>) = (r(a)/r(b)))
Proof
Definitions occuring in Statement :
ratreal: ratreal(r),
rdiv: (x/y),
req: x = y,
int-to-real: r(n),
nat_plus: ℕ+,
uall: ∀[x:A]. B[x],
pair: <a, b>,
int: ℤ
Definitions unfolded in proof :
ratreal: ratreal(r),
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
nat_plus: ℕ+,
uimplies: b supposing a,
rneq: x ≠ y,
guard: {T},
or: P ∨ Q,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
decidable: Dec(P),
not: ¬A,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
top: Top,
prop: ℙ
Lemmas referenced :
rat-to-real-req,
nat_plus_inc_int_nzero,
req_witness,
rat-to-real_wf,
rdiv_wf,
int-to-real_wf,
rless-int,
nat_plus_properties,
decidable__lt,
full-omega-unsat,
intformand_wf,
intformnot_wf,
intformless_wf,
itermConstant_wf,
itermVar_wf,
istype-int,
int_formula_prop_and_lemma,
istype-void,
int_formula_prop_not_lemma,
int_formula_prop_less_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_wf,
rless_wf,
nat_plus_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation_alt,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
applyEquality,
hypothesis,
setElimination,
rename,
because_Cache,
independent_isectElimination,
inrFormation_alt,
dependent_functionElimination,
productElimination,
independent_functionElimination,
natural_numberEquality,
unionElimination,
approximateComputation,
dependent_pairFormation_alt,
lambdaEquality_alt,
int_eqEquality,
isect_memberEquality_alt,
voidElimination,
independent_pairFormation,
universeIsType,
isectIsTypeImplies,
inhabitedIsType
Latex:
\mforall{}[a:\mBbbZ{}]. \mforall{}[b:\mBbbN{}\msupplus{}]. (ratreal(<a, b>) = (r(a)/r(b)))
Date html generated:
2019_10_30-AM-09_16_57
Last ObjectModification:
2019_01_10-PM-00_43_40
Theory : reals
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