Nuprl Lemma : equipollent-int_upper-nat
∀k:ℤ. {k...} ~ ℕ
Proof
Definitions occuring in Statement :
equipollent: A ~ B,
int_upper: {i...},
nat: ℕ,
all: ∀x:A. B[x],
int: ℤ
Definitions unfolded in proof :
all: ∀x:A. B[x],
equipollent: A ~ B,
exists: ∃x:A. B[x],
member: t ∈ T,
nat: ℕ,
uall: ∀[x:A]. B[x],
int_upper: {i...},
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
false: False,
implies: P ⇒ Q,
not: ¬A,
top: Top,
and: P ∧ Q,
prop: ℙ,
biject: Bij(A;B;f),
inject: Inj(A;B;f),
guard: {T},
ge: i ≥ j ,
surject: Surj(A;B;f)
Lemmas referenced :
add-subtract-cancel,
int_term_value_add_lemma,
itermAdd_wf,
biject_wf,
nat_wf,
equal_wf,
int_formula_prop_eq_lemma,
intformeq_wf,
decidable__equal_int,
nat_properties,
int_upper_wf,
le_wf,
int_formula_prop_wf,
int_term_value_var_lemma,
int_term_value_subtract_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_not_lemma,
int_formula_prop_and_lemma,
itermVar_wf,
itermSubtract_wf,
itermConstant_wf,
intformle_wf,
intformnot_wf,
intformand_wf,
satisfiable-full-omega-tt,
decidable__le,
int_upper_properties,
subtract_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
dependent_pairFormation,
lambdaEquality,
dependent_set_memberEquality,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
setElimination,
rename,
hypothesisEquality,
hypothesis,
dependent_functionElimination,
natural_numberEquality,
unionElimination,
independent_isectElimination,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
sqequalRule,
independent_pairFormation,
computeAll,
equalityTransitivity,
equalitySymmetry,
applyEquality,
setEquality,
because_Cache,
addEquality
Latex:
\mforall{}k:\mBbbZ{}. \{k...\} \msim{} \mBbbN{}
Date html generated:
2016_05_15-PM-05_25_41
Last ObjectModification:
2016_01_16-PM-00_26_56
Theory : general
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