Nuprl Lemma : negate-poly-constraints_wf
∀[Xs:polynomial-constraints() List]. (negate-poly-constraints(Xs) ∈ polynomial-constraints() List)
Proof
Definitions occuring in Statement :
negate-poly-constraints: negate-poly-constraints(Xs),
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-constraints: negate-poly-constraints(Xs),
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
ifthenelse: if b then t else f fi ,
subtype_rel: A ⊆r B,
polynomial-constraints: polynomial-constraints(),
so_lambda: λ2x.t[x],
so_apply: x[s],
bfalse: ff,
iff: P ⇐⇒ Q,
not: ¬A,
prop: ℙ,
rev_implies: P ⇐ Q,
false: False,
or: P ∨ Q,
nil: [],
cons: [a / b],
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2]
Lemmas referenced :
null_wf,
polynomial-constraints_wf,
bool_wf,
uiff_transitivity,
equal-wf-T-base,
assert_wf,
list_wf,
eqtt_to_assert,
assert_of_null,
cons_wf,
nil_wf,
subtype_rel_product,
iPolynomial_wf,
subtype_rel_list,
iff_transitivity,
bnot_wf,
not_wf,
iff_weakening_uiff,
eqff_to_assert,
assert_of_bnot,
list-cases,
it_wf,
unit_wf2,
equal_wf,
product_subtype_list,
list_accum_wf,
negate-poly-constraint_wf,
and-poly-constraints_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
hypothesisEquality,
lambdaFormation,
unionElimination,
equalityElimination,
equalityTransitivity,
equalitySymmetry,
baseClosed,
independent_functionElimination,
because_Cache,
productElimination,
independent_isectElimination,
independent_pairEquality,
voidEquality,
applyEquality,
lambdaEquality,
voidElimination,
independent_pairFormation,
impliesFunctionality,
dependent_functionElimination,
promote_hyp,
hypothesis_subsumption,
axiomEquality
Latex:
\mforall{}[Xs:polynomial-constraints() List]. (negate-poly-constraints(Xs) \mmember{} polynomial-constraints() List)
Date html generated:
2017_04_14-AM-09_02_58
Last ObjectModification:
2017_02_27-PM-03_43_38
Theory : omega
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