Nuprl Lemma : isr-omega
∀[n:ℕ]. ∀[eqs,ineqs:{L:ℤ List| ||L|| = (n + 1) ∈ ℤ} List]. ¬satisfiable(eqs;ineqs) supposing ↑isr(omega(eqs;ineqs))
Proof
Definitions occuring in Statement :
omega: omega(eqs;ineqs),
satisfiable-integer-problem: satisfiable(eqs;ineqs),
length: ||as||,
list: T List,
nat: ℕ,
assert: ↑b,
isr: isr(x),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
not: ¬A,
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,
uimplies: b supposing a,
not: ¬A,
implies: P ⇒ Q,
false: False,
omega: omega(eqs;ineqs),
int-constraint-problem: IntConstraints,
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
nat: ℕ,
prop: ℙ,
so_apply: x[s],
all: ∀x:A. B[x],
unit: Unit,
callbyvalueall: callbyvalueall,
has-value: (a)↓,
has-valueall: has-valueall(a),
and: P ∧ Q,
cand: A c∧ B
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,
isr-rep_int_constraint_step,
omega_step_wf,
omega_step_measure,
less_than_wf,
int-problem-dimension_wf,
unsat-omega_step,
unsat-int-problem_wf,
unsat-omega_start,
satisfiable-integer-problem_wf,
subtype_rel_list,
assert_wf,
isr_wf,
omega_wf,
equal-wf-T-base
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
thin,
sqequalHypSubstitution,
sqequalRule,
extract_by_obid,
isectElimination,
hypothesis,
independent_isectElimination,
lambdaEquality,
productEquality,
setEquality,
intEquality,
baseApply,
closedConclusion,
baseClosed,
hypothesisEquality,
applyEquality,
because_Cache,
addEquality,
setElimination,
rename,
natural_numberEquality,
independent_functionElimination,
callbyvalueReduce,
dependent_functionElimination,
independent_pairFormation,
voidElimination,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[n:\mBbbN{}]. \mforall{}[eqs,ineqs:\{L:\mBbbZ{} List| ||L|| = (n + 1)\} List].
\mneg{}satisfiable(eqs;ineqs) supposing \muparrow{}isr(omega(eqs;ineqs))
Date html generated:
2017_04_14-AM-09_12_43
Last ObjectModification:
2017_02_27-PM-03_50_00
Theory : omega
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