Nuprl Lemma : not-added-name
∀[I:fset(ℕ)]. ∀[i:ℕ]. ∀[x:names(I+i)]. x ∈ names(I) supposing x ≠ i
Proof
Definitions occuring in Statement :
add-name: I+i,
names: names(I),
fset: fset(T),
nat: ℕ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
nequal: a ≠ b ∈ T ,
member: t ∈ T,
int: ℤ
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
names: names(I),
all: ∀x:A. B[x],
uiff: uiff(P;Q),
and: P ∧ Q,
or: P ∨ Q,
nequal: a ≠ b ∈ T ,
nat: ℕ,
ge: i ≥ j ,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
implies: P ⇒ Q,
not: ¬A,
top: Top,
prop: ℙ,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
fset_wf,
add-name_wf,
names_wf,
nequal_wf,
strong-subtype-self,
le_wf,
strong-subtype-set3,
strong-subtype-deq-subtype,
int-deq_wf,
nat_wf,
fset-member_wf,
int_formula_prop_wf,
int_term_value_var_lemma,
int_formula_prop_eq_lemma,
int_formula_prop_not_lemma,
int_formula_prop_and_lemma,
itermVar_wf,
intformeq_wf,
intformnot_wf,
intformand_wf,
satisfiable-full-omega-tt,
nat_properties,
fset-member-add-name
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
setElimination,
thin,
rename,
lemma_by_obid,
dependent_functionElimination,
hypothesisEquality,
hypothesis,
productElimination,
independent_isectElimination,
unionElimination,
isectElimination,
natural_numberEquality,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
sqequalRule,
independent_pairFormation,
computeAll,
dependent_set_memberEquality,
applyEquality,
because_Cache,
axiomEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[I:fset(\mBbbN{})]. \mforall{}[i:\mBbbN{}]. \mforall{}[x:names(I+i)]. x \mmember{} names(I) supposing x \mneq{} i
Date html generated:
2016_05_18-PM-00_00_19
Last ObjectModification:
2016_01_18-PM-01_03_41
Theory : cubical!type!theory
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