Nuprl Lemma : equipollent-two
𝔹 ~ ℕ2
Proof
Definitions occuring in Statement :
equipollent: A ~ B,
int_seg: {i..j-},
bool: 𝔹,
natural_number: $n
Definitions unfolded in proof :
equipollent: A ~ B,
exists: ∃x:A. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
ifthenelse: if b then t else f fi ,
uall: ∀[x:A]. B[x],
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
int_seg: {i..j-},
lelt: i ≤ j < k,
le: A ≤ B,
less_than': less_than'(a;b),
false: False,
not: ¬A,
prop: ℙ,
less_than: a < b,
squash: ↓T,
true: True,
bfalse: ff,
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
biject: Bij(A;B;f),
inject: Inj(A;B;f),
surject: Surj(A;B;f),
satisfiable_int_formula: satisfiable_int_formula(fmla),
top: Top,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
subtype_rel: A ⊆r B,
decidable: Dec(P)
Lemmas referenced :
bool_wf,
eqtt_to_assert,
false_wf,
lelt_wf,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
int_seg_wf,
biject_wf,
btrue_wf,
equal-wf-base,
int_seg_properties,
satisfiable-full-omega-tt,
intformeq_wf,
itermConstant_wf,
int_formula_prop_eq_lemma,
int_term_value_constant_lemma,
int_formula_prop_wf,
iff_imp_equal_bool,
bfalse_wf,
assert_elim,
int_subtype_base,
assert_wf,
equal-wf-base-T,
decidable__equal_int,
intformnot_wf,
int_formula_prop_not_lemma,
equal-wf-T-base,
int_seg_subtype,
int_seg_cases,
intformand_wf,
intformless_wf,
itermVar_wf,
intformle_wf,
int_formula_prop_and_lemma,
int_formula_prop_less_lemma,
int_term_value_var_lemma,
int_formula_prop_le_lemma
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
dependent_pairFormation,
lambdaEquality,
cut,
hypothesisEquality,
hypothesis,
thin,
introduction,
extract_by_obid,
lambdaFormation,
sqequalHypSubstitution,
unionElimination,
equalityElimination,
sqequalRule,
isectElimination,
productElimination,
independent_isectElimination,
dependent_set_memberEquality,
natural_numberEquality,
independent_pairFormation,
imageMemberEquality,
baseClosed,
equalityTransitivity,
equalitySymmetry,
promote_hyp,
dependent_functionElimination,
instantiate,
cumulativity,
independent_functionElimination,
because_Cache,
voidElimination,
functionExtensionality,
applyEquality,
applyLambdaEquality,
setElimination,
rename,
intEquality,
isect_memberEquality,
voidEquality,
computeAll,
addLevel,
levelHypothesis,
hypothesis_subsumption,
addEquality,
int_eqEquality
Latex:
\mBbbB{} \msim{} \mBbbN{}2
Date html generated:
2017_04_17-AM-09_31_30
Last ObjectModification:
2017_02_27-PM-05_31_41
Theory : equipollence!!cardinality!
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