Nuprl Lemma : void-function-equipollent
∀F:Top. i:ℕ0 ⟶ F[i] ~ Top
Proof
Definitions occuring in Statement :
equipollent: A ~ B,
int_seg: {i..j-},
top: Top,
so_apply: x[s],
all: ∀x:A. B[x],
function: x:A ⟶ B[x],
natural_number: $n
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
equipollent: A ~ B,
exists: ∃x:A. B[x],
top: Top,
uall: ∀[x:A]. B[x],
guard: {T},
int_seg: {i..j-},
lelt: i ≤ j < k,
and: P ∧ Q,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
false: False,
implies: P ⇒ Q,
not: ¬A,
prop: ℙ,
biject: Bij(A;B;f),
inject: Inj(A;B;f),
surject: Surj(A;B;f),
subtype_rel: A ⊆r B
Lemmas referenced :
lelt_wf,
subtype_rel-equal,
biject_wf,
equal_wf,
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,
int_seg_wf,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
lemma_by_obid,
hypothesis,
dependent_pairFormation,
functionExtensionality,
isect_memberEquality,
voidElimination,
voidEquality,
functionEquality,
thin,
instantiate,
sqequalHypSubstitution,
isectElimination,
natural_numberEquality,
because_Cache,
hypothesisEquality,
setElimination,
rename,
productElimination,
independent_isectElimination,
lambdaEquality,
int_eqEquality,
intEquality,
dependent_functionElimination,
sqequalRule,
independent_pairFormation,
computeAll,
applyEquality,
setEquality
Latex:
\mforall{}F:Top. i:\mBbbN{}0 {}\mrightarrow{} F[i] \msim{} Top
Date html generated:
2016_05_14-PM-04_05_38
Last ObjectModification:
2016_01_14-PM-11_06_07
Theory : equipollence!!cardinality!
Home
Index