Nuprl Lemma : nat-inf-attach-unit
∀F:ℕ ⟶ Type. ∃G:ℕ∞ ⟶ Type. ((∀n:ℕ. G n∞ ~ F n) ∧ G ∞ ~ ℕ1)
Proof
Definitions occuring in Statement :
nat-inf-infinity: ∞,
nat2inf: n∞,
nat-inf: ℕ∞,
equipollent: A ~ B,
int_seg: {i..j-},
nat: ℕ,
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
and: P ∧ Q,
apply: f a,
function: x:A ⟶ B[x],
natural_number: $n,
universe: Type
Definitions unfolded in proof :
top: Top,
false: False,
satisfiable_int_formula: satisfiable_int_formula(fmla),
not: ¬A,
or: P ∨ Q,
decidable: Dec(P),
ge: i ≥ j ,
guard: {T},
sq_type: SQType(T),
nat: ℕ,
pi1: fst(t),
uimplies: b supposing a,
subtype_rel: A ⊆r B,
implies: P ⇒ Q,
singleton-type: singleton-type(A),
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
prop: ℙ,
and: P ∧ Q,
cand: A c∧ B,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
nat-inf-infinity-new,
equal-wf-base-T,
equipollent-empty-domain,
int_formula_prop_wf,
int_term_value_var_lemma,
int_formula_prop_eq_lemma,
int_formula_prop_not_lemma,
itermVar_wf,
intformeq_wf,
intformnot_wf,
full-omega-unsat,
decidable__equal_int,
nat_properties,
le_wf,
set_subtype_base,
int_subtype_base,
subtype_base_sq,
subtype_rel_self,
subtype_rel_dep_function,
equipollent-singleton-domain,
set_wf,
nat2inf-one-one,
nat_wf,
equal_wf,
nat-inf_wf,
nat2inf_wf,
all_wf,
equipollent_wf,
nat-inf-infinity_wf,
int_seg_wf
Rules used in proof :
baseClosed,
voidEquality,
voidElimination,
isect_memberEquality,
int_eqEquality,
approximateComputation,
unionElimination,
equalityTransitivity,
productElimination,
intEquality,
independent_isectElimination,
instantiate,
dependent_functionElimination,
equalitySymmetry,
independent_functionElimination,
because_Cache,
dependent_set_memberEquality,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
dependent_pairFormation,
lambdaEquality,
functionEquality,
setEquality,
cut,
introduction,
extract_by_obid,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
applyEquality,
functionExtensionality,
setElimination,
rename,
independent_pairFormation,
productEquality,
sqequalRule,
natural_numberEquality,
cumulativity,
universeEquality
Latex:
\mforall{}F:\mBbbN{} {}\mrightarrow{} Type. \mexists{}G:\mBbbN{}\minfty{} {}\mrightarrow{} Type. ((\mforall{}n:\mBbbN{}. G n\minfty{} \msim{} F n) \mwedge{} G \minfty{} \msim{} \mBbbN{}1)
Date html generated:
2018_07_29-AM-09_29_18
Last ObjectModification:
2018_07_27-PM-05_28_45
Theory : basic
Home
Index