Nuprl Lemma : pair-coding-exists
∃code:ℕ ⟶ (ℕ × ℕ). Surj(ℕ;ℕ × ℕ;code)
Proof
Definitions occuring in Statement :
surject: Surj(A;B;f),
nat: ℕ,
exists: ∃x:A. B[x],
function: x:A ⟶ B[x],
product: x:A × B[x]
Definitions unfolded in proof :
exists: ∃x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
surject: Surj(A;B;f),
all: ∀x:A. B[x],
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-pair_wf,
nat_wf,
surject_wf,
code-pair_wf,
equal_wf,
squash_wf,
true_wf,
coded-code-pair,
iff_weakening_equal
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
dependent_pairFormation,
lambdaEquality,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
lambdaFormation,
sqequalRule,
productEquality,
functionExtensionality,
applyEquality,
productElimination,
imageElimination,
equalityTransitivity,
equalitySymmetry,
universeEquality,
because_Cache,
independent_pairEquality,
natural_numberEquality,
imageMemberEquality,
baseClosed,
independent_isectElimination,
independent_functionElimination
Latex:
\mexists{}code:\mBbbN{} {}\mrightarrow{} (\mBbbN{} \mtimes{} \mBbbN{}). Surj(\mBbbN{};\mBbbN{} \mtimes{} \mBbbN{};code)
Date html generated:
2018_05_21-PM-07_56_51
Last ObjectModification:
2017_07_26-PM-05_34_27
Theory : general
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