Nuprl Lemma : equipollent-void-domain
∀[A:Type]. ℕ0 ⟶ A ~ ℕ1
Proof
Definitions occuring in Statement :
equipollent: A ~ B,
int_seg: {i..j-},
uall: ∀[x:A]. B[x],
function: x:A ⟶ B[x],
natural_number: $n,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
implies: P ⇒ Q,
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a,
not: ¬A,
guard: {T},
int_seg: {i..j-},
lelt: i ≤ j < k,
and: P ∧ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
all: ∀x:A. B[x],
top: Top,
prop: ℙ
Lemmas referenced :
int_formula_prop_wf,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_less_lemma,
int_formula_prop_and_lemma,
intformle_wf,
itermConstant_wf,
itermVar_wf,
intformless_wf,
intformand_wf,
satisfiable-full-omega-tt,
int_seg_properties,
singleton-type-void-domain,
singleton-type-one,
int_seg_wf,
equipollent-singletons
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
functionEquality,
natural_numberEquality,
hypothesis,
hypothesisEquality,
independent_functionElimination,
universeEquality,
sqequalRule,
lambdaEquality,
independent_isectElimination,
lambdaFormation,
because_Cache,
setElimination,
rename,
productElimination,
dependent_pairFormation,
int_eqEquality,
intEquality,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll
Latex:
\mforall{}[A:Type]. \mBbbN{}0 {}\mrightarrow{} A \msim{} \mBbbN{}1
Date html generated:
2016_05_14-PM-04_02_24
Last ObjectModification:
2016_01_14-PM-11_05_49
Theory : equipollence!!cardinality!
Home
Index