Nuprl Lemma : ni-eventually-equal-equiv
EquivRel(ℕ∞;f,g.ni-eventually-equal(f;g))
Proof
Definitions occuring in Statement :
ni-eventually-equal: ni-eventually-equal(f;g),
nat-inf: ℕ∞,
equiv_rel: EquivRel(T;x,y.E[x; y])
Definitions unfolded in proof :
equiv_rel: EquivRel(T;x,y.E[x; y]),
trans: Trans(T;x,y.E[x; y]),
sym: Sym(T;x,y.E[x; y]),
refl: Refl(T;x,y.E[x; y]),
and: P ∧ Q,
cand: A c∧ B,
all: ∀x:A. B[x],
ni-eventually-equal: ni-eventually-equal(f;g),
member: t ∈ T,
implies: P ⇒ Q,
uall: ∀[x:A]. B[x],
prop: ℙ,
exists: ∃x:A. B[x],
nat: ℕ,
le: A ≤ B,
less_than': less_than'(a;b),
not: ¬A,
false: False,
nat-inf: ℕ∞,
int_upper: {i...},
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
subtype_rel: A ⊆r B,
guard: {T},
sq_stable: SqStable(P),
squash: ↓T,
ge: i ≥ j ,
true: True,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
nat-inf_wf,
ni-eventually-equal_wf,
istype-void,
istype-le,
int_upper_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-int_upper,
bool_wf,
upper_subtype_nat,
sq_stable__le,
equal_wf,
squash_wf,
true_wf,
istype-universe,
nat_properties,
subtype_rel_self,
iff_weakening_equal,
imax_wf,
imax_nat,
intformeq_wf,
int_formula_prop_eq_lemma,
int_upper_subtype_int_upper,
imax_ub,
int_upper_subtype_nat
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
cut,
lambdaFormation_alt,
universeIsType,
introduction,
extract_by_obid,
hypothesis,
independent_pairFormation,
sqequalHypSubstitution,
sqequalRule,
isectElimination,
thin,
hypothesisEquality,
inhabitedIsType,
because_Cache,
dependent_pairFormation_alt,
dependent_set_memberEquality_alt,
natural_numberEquality,
voidElimination,
applyEquality,
setElimination,
rename,
dependent_functionElimination,
unionElimination,
independent_isectElimination,
approximateComputation,
independent_functionElimination,
lambdaEquality_alt,
int_eqEquality,
Error :memTop,
functionIsType,
equalityIstype,
imageMemberEquality,
baseClosed,
imageElimination,
productElimination,
equalityTransitivity,
equalitySymmetry,
instantiate,
universeEquality,
applyLambdaEquality,
inrFormation_alt,
inlFormation_alt
Latex:
EquivRel(\mBbbN{}\minfty{};f,g.ni-eventually-equal(f;g))
Date html generated:
2020_05_20-AM-07_47_53
Last ObjectModification:
2019_12_31-PM-06_32_16
Theory : basic
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