Nuprl Lemma : fresh-cname_wf
∀[I:Cname List]. (fresh-cname(I) ∈ {x:Cname| ¬(x ∈ I)} )
Proof
Definitions occuring in Statement :
fresh-cname: fresh-cname(I),
coordinate_name: Cname,
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,
int_upper: {i...},
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
not: ¬A,
implies: P ⇒ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
prop: ℙ,
false: False,
subtype_rel: A ⊆r B,
coordinate_name: Cname,
so_lambda: λ2x.t[x],
so_apply: x[s],
and: P ∧ Q,
fresh-cname: fresh-cname(I),
nat_plus: ℕ+,
guard: {T},
uiff: uiff(P;Q),
ge: i ≥ j ,
le: A ≤ B,
pi1: fst(t),
l_member: (x ∈ l),
l_all: (∀x∈L.P[x]),
cand: A c∧ B,
int_seg: {i..j-},
nat: ℕ,
squash: ↓T,
lelt: i ≤ j < k,
less_than: a < b,
true: True,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
cons_wf,
int_upper_wf,
decidable__le,
full-omega-unsat,
intformnot_wf,
intformle_wf,
itermConstant_wf,
istype-int,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_formula_prop_wf,
istype-le,
subtype_rel_list,
coordinate_name_wf,
subtype_rel_sets_simple,
le_wf,
intformand_wf,
itermVar_wf,
int_formula_prop_and_lemma,
int_term_value_var_lemma,
list_wf,
list-max-property,
istype-int_upper,
length_of_cons_lemma,
add_nat_plus,
length_wf_nat,
decidable__lt,
intformless_wf,
int_formula_prop_less_lemma,
istype-less_than,
nat_plus_properties,
add-is-int-iff,
itermAdd_wf,
intformeq_wf,
int_term_value_add_lemma,
int_formula_prop_eq_lemma,
false_wf,
list-max_wf,
non_neg_length,
length_wf,
l_member_wf,
int_upper_properties,
set_subtype_base,
equal-wf-base,
int_subtype_base,
l_all_wf2,
istype-void,
nat_properties,
squash_wf,
true_wf,
select_cons_tl,
subtype_rel_self,
iff_weakening_equal,
add-subtract-cancel,
select_cons_tl_sq2
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
natural_numberEquality,
hypothesis,
dependent_set_memberEquality_alt,
dependent_functionElimination,
unionElimination,
independent_isectElimination,
approximateComputation,
independent_functionElimination,
dependent_pairFormation_alt,
lambdaEquality_alt,
Error :memTop,
sqequalRule,
universeIsType,
hypothesisEquality,
voidElimination,
applyEquality,
intEquality,
lambdaFormation_alt,
int_eqEquality,
independent_pairFormation,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
setElimination,
rename,
inhabitedIsType,
applyLambdaEquality,
pointwiseFunctionality,
promote_hyp,
baseApply,
closedConclusion,
baseClosed,
productElimination,
equalityIstype,
because_Cache,
addEquality,
productIsType,
sqequalBase,
setIsType,
functionIsType,
imageMemberEquality,
imageElimination,
instantiate,
universeEquality
Latex:
\mforall{}[I:Cname List]. (fresh-cname(I) \mmember{} \{x:Cname| \mneg{}(x \mmember{} I)\} )
Date html generated:
2020_05_21-AM-10_48_10
Last ObjectModification:
2020_01_01-PM-02_24_19
Theory : cubical!sets
Home
Index