Nuprl Lemma : normalize-constraints-eq
∀[k:ℕ]. ∀[A:(ℕ ⟶ ℚ × ℤ) List]. (normalize-constraints(k;A) = A ∈ ((ℕ ⟶ ℚ × ℤ) List))
Proof
Definitions occuring in Statement :
normalize-constraints: normalize-constraints(k;A),
rationals: ℚ,
list: T List,
nat: ℕ,
uall: ∀[x:A]. B[x],
function: x:A ⟶ B[x],
product: x:A × B[x],
int: ℤ,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
all: ∀x:A. B[x],
implies: P ⇒ Q,
prop: ℙ,
exists: ∃x:A. B[x],
nat: ℕ,
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
false: False,
not: ¬A,
squash: ↓T,
normalize-constraints: normalize-constraints(k;A),
so_lambda: λ2x.t[x],
so_apply: x[s],
callbyvalueall: callbyvalueall,
has-value: (a)↓,
has-valueall: has-valueall(a)
Lemmas referenced :
evalall-reduce,
int-valueall-type,
function-valueall-type,
product-valueall-type,
list-valueall-type,
valueall-type-has-valueall,
value-type_wf,
rationals-value-type,
le_wf,
false_wf,
list_wf,
l_member_wf,
normalize-constraint-eq,
normalize-constraint_wf,
rationals_wf,
nat_wf,
trivial_map
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
productEquality,
functionEquality,
hypothesis,
intEquality,
hypothesisEquality,
lambdaEquality,
independent_isectElimination,
lambdaFormation,
sqequalRule,
because_Cache,
isect_memberEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
dependent_pairFormation,
dependent_set_memberEquality,
natural_numberEquality,
independent_pairFormation,
imageMemberEquality,
baseClosed,
independent_functionElimination,
callbyvalueReduce
Latex:
\mforall{}[k:\mBbbN{}]. \mforall{}[A:(\mBbbN{} {}\mrightarrow{} \mBbbQ{} \mtimes{} \mBbbZ{}) List]. (normalize-constraints(k;A) = A)
Date html generated:
2016_05_15-PM-11_24_25
Last ObjectModification:
2016_01_16-PM-09_15_00
Theory : rationals
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