Nuprl Lemma : negate-poly-constraint_wf
∀[X:polynomial-constraints()]. (negate-poly-constraint(X) ∈ polynomial-constraints() List)
Proof
Definitions occuring in Statement :
negate-poly-constraint: negate-poly-constraint(X),
polynomial-constraints: polynomial-constraints(),
list: T List,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
negate-poly-constraint: negate-poly-constraint(X),
polynomial-constraints: polynomial-constraints(),
int_nzero: ℤ-o,
true: True,
nequal: a ≠ b ∈ T ,
not: ¬A,
implies: P ⇒ Q,
uimplies: b supposing a,
sq_type: SQType(T),
all: ∀x:A. B[x],
guard: {T},
false: False,
prop: ℙ,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2]
Lemmas referenced :
list_accum_wf,
iPolynomial_wf,
list_wf,
polynomial-constraints_wf,
map_wf,
nil_wf,
cons_wf,
minus-poly_wf,
add-ipoly_wf,
const-poly_wf,
subtype_base_sq,
int_subtype_base,
equal_wf,
true_wf,
nequal_wf,
subtype_rel_product,
subtype_rel_list,
subtype_rel_self
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
sqequalHypSubstitution,
productElimination,
thin,
lemma_by_obid,
isectElimination,
hypothesis,
hypothesisEquality,
because_Cache,
lambdaEquality,
independent_pairEquality,
voidEquality,
dependent_set_memberEquality,
natural_numberEquality,
addLevel,
lambdaFormation,
instantiate,
cumulativity,
intEquality,
independent_isectElimination,
dependent_functionElimination,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination,
voidElimination,
applyEquality,
minusEquality,
axiomEquality
Latex:
\mforall{}[X:polynomial-constraints()]. (negate-poly-constraint(X) \mmember{} polynomial-constraints() List)
Date html generated:
2016_05_14-AM-07_08_49
Last ObjectModification:
2015_12_26-PM-01_07_49
Theory : omega
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