Nuprl Lemma : mk-rational_wf
∀[a:ℤ]. ∀[b:ℤ-o]. (mk-rational(a;b) ∈ ℚ)
Proof
Definitions occuring in Statement :
mk-rational: mk-rational(a;b),
rationals: ℚ,
int_nzero: ℤ-o,
uall: ∀[x:A]. B[x],
member: t ∈ T,
int: ℤ
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
mk-rational: mk-rational(a;b),
qeq: qeq(r;s),
rationals: ℚ,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
uimplies: b supposing a,
all: ∀x:A. B[x],
implies: P ⇒ Q,
b-union: A ⋃ B,
tunion: ⋃x:A.B[x],
ifthenelse: if b then t else f fi ,
bfalse: ff,
pi2: snd(t),
so_lambda: λ2x.t[x],
so_apply: x[s],
int_nzero: ℤ-o,
callbyvalueall: callbyvalueall,
has-value: (a)↓,
has-valueall: has-valueall(a),
uiff: uiff(P;Q),
and: P ∧ Q,
rev_uimplies: rev_uimplies(P;Q)
Lemmas referenced :
assert_of_eq_int,
eq_int_wf,
eqtt_to_assert,
evalall-reduce,
nequal_wf,
set-valueall-type,
int-valueall-type,
product-valueall-type,
valueall-type-has-valueall,
ifthenelse_wf,
bfalse_wf,
quotient-member-eq,
qeq-equiv,
btrue_wf,
qeq_wf,
bool_wf,
equal_wf,
b-union_wf,
int_nzero_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
hypothesis,
sqequalRule,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
lemma_by_obid,
isect_memberEquality,
isectElimination,
thin,
hypothesisEquality,
because_Cache,
intEquality,
productEquality,
lambdaEquality,
independent_isectElimination,
dependent_functionElimination,
independent_functionElimination,
imageMemberEquality,
dependent_pairEquality,
independent_pairEquality,
instantiate,
universeEquality,
baseClosed,
lambdaFormation,
natural_numberEquality,
callbyvalueReduce,
multiplyEquality,
setElimination,
rename,
productElimination
Latex:
\mforall{}[a:\mBbbZ{}]. \mforall{}[b:\mBbbZ{}\msupminus{}\msupzero{}]. (mk-rational(a;b) \mmember{} \mBbbQ{})
Date html generated:
2016_05_15-PM-10_37_56
Last ObjectModification:
2016_01_16-PM-09_37_05
Theory : rationals
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