Nuprl Lemma : finite-sequence-coding-exists
∃code:ℕ ⟶ (k:ℕ × (ℕk ⟶ ℕ)). Surj(ℕ;k:ℕ × (ℕk ⟶ ℕ);code)
Proof
Definitions occuring in Statement :
surject: Surj(A;B;f),
int_seg: {i..j-},
nat: ℕ,
exists: ∃x:A. B[x],
function: x:A ⟶ B[x],
product: x:A × B[x],
natural_number: $n
Definitions unfolded in proof :
exists: ∃x:A. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
surject: Surj(A;B;f),
uall: ∀[x:A]. B[x],
nat: ℕ,
prop: ℙ,
squash: ↓T,
true: True,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q
Lemmas referenced :
coded-seq_wf,
nat_wf,
int_seg_wf,
surject_wf,
code-seq_wf,
equal_wf,
squash_wf,
true_wf,
coded-code-seq,
iff_weakening_equal
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
dependent_pairFormation,
lambdaEquality,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
hypothesis,
lambdaFormation,
productElimination,
sqequalRule,
productEquality,
functionEquality,
isectElimination,
natural_numberEquality,
setElimination,
rename,
functionExtensionality,
applyEquality,
imageElimination,
equalityTransitivity,
equalitySymmetry,
universeEquality,
because_Cache,
dependent_pairEquality,
imageMemberEquality,
baseClosed,
independent_isectElimination,
independent_functionElimination
Latex:
\mexists{}code:\mBbbN{} {}\mrightarrow{} (k:\mBbbN{} \mtimes{} (\mBbbN{}k {}\mrightarrow{} \mBbbN{})). Surj(\mBbbN{};k:\mBbbN{} \mtimes{} (\mBbbN{}k {}\mrightarrow{} \mBbbN{});code)
Date html generated:
2018_05_21-PM-07_57_00
Last ObjectModification:
2017_07_26-PM-05_34_38
Theory : general
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