Nuprl Lemma : surject-nat-bool
∃g:ℕ ⟶ 𝔹. Surj(ℕ;𝔹;g)
Proof
Definitions occuring in Statement :
surject: Surj(A;B;f),
nat: ℕ,
bool: 𝔹,
exists: ∃x:A. B[x],
function: x:A ⟶ B[x]
Definitions unfolded in proof :
nequal: a ≠ b ∈ T ,
true: True,
not: ¬A,
less_than': less_than'(a;b),
le: A ≤ B,
false: False,
assert: ↑b,
ifthenelse: if b then t else f fi ,
bnot: ¬bb,
guard: {T},
sq_type: SQType(T),
or: P ∨ Q,
prop: ℙ,
bfalse: ff,
uimplies: b supposing a,
and: P ∧ Q,
uiff: uiff(P;Q),
btrue: tt,
it: ⋅,
unit: Unit,
bool: 𝔹,
implies: P ⇒ Q,
all: ∀x:A. B[x],
surject: Surj(A;B;f),
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
exists: ∃x:A. B[x]
Lemmas referenced :
equal-wf-T-base,
neg_assert_of_eq_int,
int_subtype_base,
assert_of_eq_int,
le_wf,
false_wf,
surject_wf,
assert-bnot,
bool_subtype_base,
subtype_base_sq,
bool_cases_sqequal,
equal_wf,
eqff_to_assert,
eqtt_to_assert,
nat_wf,
btrue_wf,
bfalse_wf,
bool_wf,
eq_int_wf,
ifthenelse_wf
Rules used in proof :
baseClosed,
intEquality,
independent_pairFormation,
dependent_set_memberEquality,
applyEquality,
functionExtensionality,
voidElimination,
because_Cache,
independent_functionElimination,
equalitySymmetry,
equalityTransitivity,
cumulativity,
instantiate,
dependent_functionElimination,
promote_hyp,
independent_isectElimination,
productElimination,
equalityElimination,
unionElimination,
sqequalRule,
lambdaFormation,
natural_numberEquality,
hypothesis,
hypothesisEquality,
rename,
setElimination,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
introduction,
cut,
lambdaEquality,
dependent_pairFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mexists{}g:\mBbbN{} {}\mrightarrow{} \mBbbB{}. Surj(\mBbbN{};\mBbbB{};g)
Date html generated:
2017_09_29-PM-05_48_02
Last ObjectModification:
2017_09_04-PM-00_14_35
Theory : fun_1
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