Nuprl Lemma : equipollent-non-zero
∀[T:Type]. ∀n:ℕ+. (T ~ ℕn ⇒ T)
Proof
Definitions occuring in Statement :
equipollent: A ~ B,
int_seg: {i..j-},
nat_plus: ℕ+,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
natural_number: $n,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
equipollent: A ~ B,
exists: ∃x:A. B[x],
biject: Bij(A;B;f),
and: P ∧ Q,
surject: Surj(A;B;f),
member: t ∈ T,
int_seg: {i..j-},
lelt: i ≤ j < k,
le: A ≤ B,
less_than': less_than'(a;b),
false: False,
not: ¬A,
prop: ℙ,
nat_plus: ℕ+,
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
top: Top
Lemmas referenced :
nat_plus_wf,
int_seg_wf,
equipollent_wf,
lelt_wf,
int_formula_prop_wf,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_formula_prop_less_lemma,
int_formula_prop_not_lemma,
int_formula_prop_and_lemma,
itermVar_wf,
itermConstant_wf,
intformless_wf,
intformnot_wf,
intformand_wf,
satisfiable-full-omega-tt,
decidable__lt,
nat_plus_properties,
false_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
sqequalHypSubstitution,
productElimination,
thin,
dependent_functionElimination,
dependent_set_memberEquality,
natural_numberEquality,
independent_pairFormation,
sqequalRule,
hypothesis,
cut,
lemma_by_obid,
isectElimination,
hypothesisEquality,
setElimination,
rename,
unionElimination,
independent_isectElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
computeAll,
universeEquality,
introduction
Latex:
\mforall{}[T:Type]. \mforall{}n:\mBbbN{}\msupplus{}. (T \msim{} \mBbbN{}n {}\mRightarrow{} T)
Date html generated:
2016_05_14-PM-04_01_48
Last ObjectModification:
2016_01_14-PM-11_06_04
Theory : equipollence!!cardinality!
Home
Index