Nuprl Lemma : maybe-new_wf
∀[s:Name]. ∀[avoid:Name List]. (maybe-new(s;avoid) ∈ {s':Name| ¬(s' ∈ avoid)} )
Proof
Definitions occuring in Statement :
maybe-new: maybe-new(s;avoid),
name: Name,
l_member: (x ∈ l),
list: T List,
uall: ∀[x:A]. B[x],
not: ¬A,
member: t ∈ T,
set: {x:A| B[x]}
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
maybe-new: maybe-new(s;avoid),
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
iff: P ⇐⇒ Q,
and: P ∧ Q,
prop: ℙ,
rev_implies: P ⇐ Q,
ifthenelse: if b then t else f fi ,
let: let,
bfalse: ff,
not: ¬A,
false: False,
name: Name,
name-deq: NameDeq,
so_lambda: λ2x.t[x],
so_apply: x[s],
exists: ∃x:A. B[x],
subtype_rel: A ⊆r B,
uimplies: b supposing a,
le: A ≤ B,
less_than': less_than'(a;b),
decidable: Dec(P),
or: P ∨ Q,
l_member: (x ∈ l),
cand: A c∧ B,
nat: ℕ,
guard: {T},
int_seg: {i..j-},
ge: i ≥ j ,
lelt: i ≤ j < k,
satisfiable_int_formula: satisfiable_int_formula(fmla),
top: Top,
pi1: fst(t),
uiff: uiff(P;Q),
inject: Inj(A;B;f),
squash: ↓T,
true: True
Lemmas referenced :
deq-member_wf,
name_wf,
name-deq_wf,
bool_wf,
iff_transitivity,
equal-wf-T-base,
assert_wf,
l_member_wf,
iff_weakening_uiff,
eqtt_to_assert,
assert-deq-member,
bnot_wf,
not_wf,
eqff_to_assert,
assert_of_bnot,
equal_wf,
list_wf,
list-deq_wf,
atom-deq_wf,
append_wf,
nat-to-str_wf,
exists_wf,
nat_wf,
decidable__exists_int_seg,
length_wf,
int_seg_subtype_nat,
false_wf,
int_seg_wf,
decidable__not,
decidable__l_member,
decidable__equal_list,
decidable__atom_equal,
less_than_wf,
select_wf,
nat_properties,
int_seg_properties,
decidable__le,
satisfiable-full-omega-tt,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_wf,
all_wf,
non_neg_length,
lelt_wf,
length_wf_nat,
pigeon-hole,
add_nat_wf,
le_wf,
add-is-int-iff,
itermAdd_wf,
intformeq_wf,
int_term_value_add_lemma,
int_formula_prop_eq_lemma,
squash_wf,
true_wf,
iff_weakening_equal,
decidable__equal_int,
str-to-nat-to-str,
str-to-nat_wf,
general-append-cancellation,
mu-property,
deq_wf,
mu_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,
independent_pairFormation,
dependent_functionElimination,
productElimination,
impliesFunctionality,
voidElimination,
dependent_set_memberEquality,
axiomEquality,
isect_memberEquality,
atomEquality,
lambdaEquality,
addLevel,
existsFunctionality,
instantiate,
natural_numberEquality,
addEquality,
applyEquality,
independent_isectElimination,
dependent_pairFormation,
promote_hyp,
productEquality,
setElimination,
rename,
int_eqEquality,
intEquality,
voidEquality,
computeAll,
functionExtensionality,
applyLambdaEquality,
pointwiseFunctionality,
baseApply,
closedConclusion,
imageElimination,
universeEquality,
imageMemberEquality,
cumulativity,
inlFormation
Latex:
\mforall{}[s:Name]. \mforall{}[avoid:Name List]. (maybe-new(s;avoid) \mmember{} \{s':Name| \mneg{}(s' \mmember{} avoid)\} )
Date html generated:
2017_04_17-AM-09_18_29
Last ObjectModification:
2017_02_27-PM-05_22_42
Theory : decidable!equality
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