Nuprl Lemma : omega_wf
∀[n:ℕ]. ∀[eqs,ineqs:{L:ℤ List| ||L|| = (n + 1) ∈ ℤ} List]. (omega(eqs;ineqs) ∈ {p:IntConstraints| dim(p) = 0 ∈ ℤ} )
Proof
Definitions occuring in Statement :
omega: omega(eqs;ineqs),
int-problem-dimension: dim(p),
int-constraint-problem: IntConstraints,
length: ||as||,
list: T List,
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
set: {x:A| B[x]} ,
add: n + m,
natural_number: $n,
int: ℤ,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
omega: omega(eqs;ineqs),
uimplies: b supposing a,
int-constraint-problem: IntConstraints,
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
nat: ℕ,
prop: ℙ,
so_apply: x[s],
implies: P ⇒ Q,
all: ∀x:A. B[x],
unit: Unit,
callbyvalueall: callbyvalueall,
has-value: (a)↓,
has-valueall: has-valueall(a)
Lemmas referenced :
valueall-type-has-valueall,
int-constraint-problem_wf,
union-valueall-type,
tunion_wf,
nat_wf,
list_wf,
equal-wf-base-T,
unit_wf2,
tunion-valueall-type,
product-valueall-type,
list-valueall-type,
set-valueall-type,
int-valueall-type,
equal-valueall-type,
omega_start_wf,
evalall-reduce,
rep_int_constraint_step_wf,
omega_step_measure,
less_than_wf,
int-problem-dimension_wf,
list_subtype_base,
int_subtype_base
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
independent_isectElimination,
lambdaEquality,
productEquality,
setEquality,
intEquality,
because_Cache,
baseApply,
closedConclusion,
baseClosed,
hypothesisEquality,
applyEquality,
addEquality,
setElimination,
rename,
natural_numberEquality,
independent_functionElimination,
lambdaFormation,
callbyvalueReduce,
dependent_functionElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality
Latex:
\mforall{}[n:\mBbbN{}]. \mforall{}[eqs,ineqs:\{L:\mBbbZ{} List| ||L|| = (n + 1)\} List].
(omega(eqs;ineqs) \mmember{} \{p:IntConstraints| dim(p) = 0\} )
Date html generated:
2017_04_14-AM-09_12_38
Last ObjectModification:
2017_02_27-PM-03_49_57
Theory : omega
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