Nuprl Lemma : normalize-constraint_wf
∀[k:ℕ]. ∀[A:ℕ ⟶ ℚ × ℤ]. (normalize-constraint(k;A) ∈ ℕ ⟶ ℚ × ℤ)
Proof
Definitions occuring in Statement :
normalize-constraint: normalize-constraint(k;p),
rationals: ℚ,
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ⟶ B[x],
product: x:A × B[x],
int: ℤ
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
normalize-constraint: normalize-constraint(k;p),
has-value: (a)↓,
uimplies: b supposing a,
nat: ℕ,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
prop: ℙ,
all: ∀x:A. B[x],
callbyvalueall: callbyvalueall,
has-valueall: has-valueall(a)
Lemmas referenced :
value-type-has-value,
int-value-type,
valueall-type-has-valueall,
list_wf,
rationals_wf,
list-valueall-type,
rationals-valueall-type,
map_wf,
int_seg_wf,
subtype_rel_dep_function,
nat_wf,
int_seg_subtype_nat,
false_wf,
subtype_rel_self,
upto_wf,
evalall-reduce,
select?_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
productElimination,
thin,
callbyvalueReduce,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
intEquality,
independent_isectElimination,
hypothesis,
hypothesisEquality,
natural_numberEquality,
setElimination,
rename,
applyEquality,
lambdaEquality,
independent_pairFormation,
lambdaFormation,
because_Cache,
independent_pairEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
productEquality,
functionEquality,
isect_memberEquality
Latex:
\mforall{}[k:\mBbbN{}]. \mforall{}[A:\mBbbN{} {}\mrightarrow{} \mBbbQ{} \mtimes{} \mBbbZ{}]. (normalize-constraint(k;A) \mmember{} \mBbbN{} {}\mrightarrow{} \mBbbQ{} \mtimes{} \mBbbZ{})
Date html generated:
2016_05_15-PM-11_24_02
Last ObjectModification:
2015_12_27-PM-07_30_37
Theory : rationals
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