Nuprl Lemma : new-name_wf
∀[I:fset(ℕ)]. (new-name(I) ∈ {i:ℕ| ¬i ∈ I} )
Proof
Definitions occuring in Statement :
new-name: new-name(I),
fset-member: a ∈ s,
fset: fset(T),
int-deq: IntDeq,
nat: ℕ,
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,
new-name: new-name(I),
nat: ℕ,
uimplies: b supposing a,
all: ∀x:A. B[x],
subtype_rel: A ⊆r B,
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
prop: ℙ,
guard: {T},
ge: i ≥ j ,
decidable: Dec(P),
or: P ∨ Q,
uiff: uiff(P;Q),
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
top: Top,
so_lambda: λ2x.t[x],
so_apply: x[s],
nat-deq: NatDeq,
int-deq: IntDeq
Lemmas referenced :
fset-max_wf,
decidable__equal_nat,
nat_wf,
add_nat_wf,
false_wf,
le_wf,
nat_properties,
decidable__le,
add-is-int-iff,
satisfiable-full-omega-tt,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
itermAdd_wf,
intformeq_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_term_value_add_lemma,
int_formula_prop_eq_lemma,
int_formula_prop_wf,
equal_wf,
not_wf,
fset-member_wf,
int-deq_wf,
strong-subtype-deq-subtype,
strong-subtype-set3,
strong-subtype-self,
fset_wf,
fset-max_property,
nat-deq_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
dependent_set_memberEquality,
addEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
because_Cache,
independent_isectElimination,
lambdaFormation,
dependent_functionElimination,
hypothesis,
applyEquality,
natural_numberEquality,
hypothesisEquality,
lambdaEquality,
independent_pairFormation,
equalityTransitivity,
equalitySymmetry,
applyLambdaEquality,
setElimination,
rename,
unionElimination,
pointwiseFunctionality,
promote_hyp,
baseApply,
closedConclusion,
baseClosed,
productElimination,
dependent_pairFormation,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
computeAll,
independent_functionElimination,
axiomEquality
Latex:
\mforall{}[I:fset(\mBbbN{})]. (new-name(I) \mmember{} \{i:\mBbbN{}| \mneg{}i \mmember{} I\} )
Date html generated:
2017_10_05-AM-01_02_00
Last ObjectModification:
2017_07_28-AM-09_26_04
Theory : cubical!type!theory
Home
Index