Nuprl Lemma : biject-bool-nsub2
∃f:𝔹 ⟶ ℕ2. Bij(𝔹;ℕ2;f)
Proof
Definitions occuring in Statement :
biject: Bij(A;B;f),
int_seg: {i..j-},
bool: 𝔹,
exists: ∃x:A. B[x],
function: x:A ⟶ B[x],
natural_number: $n
Definitions unfolded in proof :
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),
decidable: Dec(P),
subtype_rel: A ⊆r B
Lemmas referenced :
eqtt_to_assert,
false_wf,
lelt_wf,
eqff_to_assert,
bool_cases_sqequal,
subtype_base_sq,
bool_wf,
bool_subtype_base,
assert-bnot,
int_seg_wf,
biject_wf,
btrue_wf,
le_antisymmetry_iff,
bfalse_wf,
decidable__int_equal,
int_subtype_base,
int_seg_properties,
int_seg_subtype_special,
int_seg_cases,
less_than_transitivity1,
less_than_irreflexivity
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :dependent_pairFormation_alt,
Error :lambdaEquality_alt,
cut,
hypothesisEquality,
hypothesis,
Error :inhabitedIsType,
Error :lambdaFormation_alt,
thin,
sqequalHypSubstitution,
unionElimination,
equalityElimination,
sqequalRule,
introduction,
extract_by_obid,
isectElimination,
productElimination,
independent_isectElimination,
Error :dependent_set_memberEquality_alt,
natural_numberEquality,
independent_pairFormation,
Error :universeIsType,
imageMemberEquality,
baseClosed,
equalityTransitivity,
equalitySymmetry,
Error :equalityIsType1,
promote_hyp,
dependent_functionElimination,
instantiate,
cumulativity,
independent_functionElimination,
because_Cache,
voidElimination,
Error :equalityIsType4,
applyLambdaEquality,
setElimination,
rename,
intEquality,
baseApply,
closedConclusion,
applyEquality,
hypothesis_subsumption
Latex:
\mexists{}f:\mBbbB{} {}\mrightarrow{} \mBbbN{}2. Bij(\mBbbB{};\mBbbN{}2;f)
Date html generated:
2019_06_20-PM-00_26_43
Last ObjectModification:
2018_09_29-PM-11_14_09
Theory : fun_1
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