Nuprl Lemma : update-assignment_wf
∀[vs:ℤ List]. ∀[z:ℤ]. ∀[Dom:Type]. ∀[a:FOAssignment(filter(λx.(¬b(x =z z));vs),Dom)]. ∀[v:Dom].
  (a[z := v] ∈ FOAssignment(vs,Dom))
Proof
Definitions occuring in Statement : 
update-assignment: a[x := v]
, 
FOAssignment: FOAssignment(vs,Dom)
, 
filter: filter(P;l)
, 
list: T List
, 
bnot: ¬bb
, 
eq_int: (i =z j)
, 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
lambda: λx.A[x]
, 
int: ℤ
, 
universe: Type
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
FOAssignment: FOAssignment(vs,Dom)
, 
update-assignment: a[x := v]
, 
all: ∀x:A. B[x]
, 
prop: ℙ
, 
implies: P 
⇒ Q
, 
bool: 𝔹
, 
unit: Unit
, 
it: ⋅
, 
btrue: tt
, 
ifthenelse: if b then t else f fi 
, 
bfalse: ff
, 
uiff: uiff(P;Q)
, 
and: P ∧ Q
, 
uimplies: b supposing a
, 
exists: ∃x:A. B[x]
, 
or: P ∨ Q
, 
sq_type: SQType(T)
, 
guard: {T}
, 
bnot: ¬bb
, 
assert: ↑b
, 
false: False
, 
iff: P 
⇐⇒ Q
, 
rev_implies: P 
⇐ Q
, 
not: ¬A
, 
nequal: a ≠ b ∈ T 
Lemmas referenced : 
l_member_wf, 
eq_int_wf, 
bool_wf, 
eqff_to_assert, 
equal_wf, 
bool_cases_sqequal, 
subtype_base_sq, 
bool_subtype_base, 
assert-bnot, 
neg_assert_of_eq_int, 
filter_wf5, 
bnot_wf, 
member_filter, 
iff_transitivity, 
assert_wf, 
not_wf, 
iff_weakening_uiff, 
assert_of_bnot, 
assert_of_eq_int, 
FOAssignment_wf, 
list_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation, 
introduction, 
cut, 
sqequalHypSubstitution, 
lambdaEquality, 
lambdaFormation, 
extract_by_obid, 
isectElimination, 
thin, 
intEquality, 
hypothesisEquality, 
hypothesis, 
setElimination, 
rename, 
unionElimination, 
equalityElimination, 
sqequalRule, 
productElimination, 
independent_isectElimination, 
equalityTransitivity, 
equalitySymmetry, 
dependent_pairFormation, 
promote_hyp, 
dependent_functionElimination, 
instantiate, 
cumulativity, 
independent_functionElimination, 
because_Cache, 
voidElimination, 
applyEquality, 
functionExtensionality, 
setEquality, 
dependent_set_memberEquality, 
independent_pairFormation, 
impliesFunctionality, 
axiomEquality, 
isect_memberEquality, 
universeEquality
Latex:
\mforall{}[vs:\mBbbZ{}  List].  \mforall{}[z:\mBbbZ{}].  \mforall{}[Dom:Type].  \mforall{}[a:FOAssignment(filter(\mlambda{}x.(\mneg{}\msubb{}(x  =\msubz{}  z));vs),Dom)].  \mforall{}[v:Dom].
    (a[z  :=  v]  \mmember{}  FOAssignment(vs,Dom))
Date html generated:
2018_05_21-PM-10_20_31
Last ObjectModification:
2017_07_26-PM-06_37_30
Theory : minimal-first-order-logic
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