Nuprl Lemma : FOQuantifier_wf
∀[vs:ℤ List]. ∀[isall:𝔹].
(FOQuantifier(isall) ∈ z:ℤ ⟶ AbstractFOFormula(vs) ⟶ AbstractFOFormula(filter(λx.(¬b(x =z z));vs)))
Proof
Definitions occuring in Statement :
FOQuantifier: FOQuantifier(isall),
AbstractFOFormula: AbstractFOFormula(vs),
filter: filter(P;l),
list: T List,
bnot: ¬bb,
eq_int: (i =z j),
bool: 𝔹,
uall: ∀[x:A]. B[x],
member: t ∈ T,
lambda: λx.A[x],
function: x:A ⟶ B[x],
int: ℤ
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
AbstractFOFormula: AbstractFOFormula(vs),
FOQuantifier: FOQuantifier(isall),
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 ,
so_lambda: λ2x.t[x],
so_apply: x[s],
prop: ℙ,
subtype_rel: A ⊆r B,
bfalse: ff
Lemmas referenced :
eqtt_to_assert,
all_wf,
FOSatWith_wf,
update-assignment_wf,
FOAssignment_wf,
filter_wf5,
l_member_wf,
bnot_wf,
eq_int_wf,
FOStruct_wf,
uiff_transitivity,
equal-wf-T-base,
bool_wf,
assert_wf,
not_wf,
eqff_to_assert,
assert_of_bnot,
exists_wf,
equal_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
hypothesisEquality,
thin,
because_Cache,
lambdaFormation,
sqequalHypSubstitution,
unionElimination,
equalityElimination,
extract_by_obid,
isectElimination,
hypothesis,
productElimination,
independent_isectElimination,
lambdaEquality,
cumulativity,
intEquality,
setElimination,
rename,
setEquality,
universeEquality,
functionEquality,
applyEquality,
baseClosed,
independent_functionElimination,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
axiomEquality,
isect_memberEquality
Latex:
\mforall{}[vs:\mBbbZ{} List]. \mforall{}[isall:\mBbbB{}].
(FOQuantifier(isall) \mmember{} z:\mBbbZ{}
{}\mrightarrow{} AbstractFOFormula(vs)
{}\mrightarrow{} AbstractFOFormula(filter(\mlambda{}x.(\mneg{}\msubb{}(x =\msubz{} z));vs)))
Date html generated:
2018_05_21-PM-10_20_39
Last ObjectModification:
2017_07_26-PM-06_37_33
Theory : minimal-first-order-logic
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