Nuprl Lemma : fresh-nat-exists2
∀L:ℕ List. ∃n:ℕ. (¬(n ∈ L))
Proof
Definitions occuring in Statement :
l_member: (x ∈ l),
list: T List,
nat: ℕ,
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
not: ¬A
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
exists: ∃x:A. B[x],
not: ¬A,
implies: P ⇒ Q,
l_member: (x ∈ l),
cand: A c∧ B,
uall: ∀[x:A]. B[x],
prop: ℙ,
false: False,
int_seg: {i..j-},
nat: ℕ,
lelt: i ≤ j < k,
and: P ∧ Q,
guard: {T},
ge: i ≥ j ,
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
top: Top
Lemmas referenced :
fresh-nat-exists,
l_member_wf,
nat_wf,
istype-void,
list_wf,
nat_properties,
decidable__le,
full-omega-unsat,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
istype-int,
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,
istype-le,
istype-less_than,
length_wf,
intformless_wf,
intformeq_wf,
int_formula_prop_less_lemma,
int_formula_prop_eq_lemma
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :lambdaFormation_alt,
hypothesis,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
productElimination,
Error :dependent_pairFormation_alt,
Error :universeIsType,
isectElimination,
sqequalRule,
Error :functionIsType,
Error :dependent_set_memberEquality_alt,
setElimination,
rename,
independent_pairFormation,
applyLambdaEquality,
natural_numberEquality,
unionElimination,
independent_isectElimination,
approximateComputation,
independent_functionElimination,
Error :lambdaEquality_alt,
int_eqEquality,
Error :isect_memberEquality_alt,
voidElimination,
Error :productIsType,
because_Cache,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}L:\mBbbN{} List. \mexists{}n:\mBbbN{}. (\mneg{}(n \mmember{} L))
Date html generated:
2019_06_20-PM-01_19_36
Last ObjectModification:
2019_03_26-PM-00_53_48
Theory : list_1
Home
Index