Nuprl Lemma : equipollent-nat-sequences
ℕ ~ k:ℕ × (ℕk ⟶ ℕ)
Proof
Definitions occuring in Statement :
equipollent: A ~ B,
int_seg: {i..j-},
nat: ℕ,
function: x:A ⟶ B[x],
product: x:A × B[x],
natural_number: $n
Definitions unfolded in proof :
equipollent: A ~ B,
exists: ∃x:A. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
prop: ℙ,
uall: ∀[x:A]. B[x],
nat: ℕ
Lemmas referenced :
coded-seq_wf,
nat_wf,
code-seq-bijection,
biject_wf,
int_seg_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
dependent_pairFormation,
lambdaEquality,
cut,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
hypothesis,
isectElimination,
productEquality,
functionEquality,
natural_numberEquality,
setElimination,
rename
Latex:
\mBbbN{} \msim{} k:\mBbbN{} \mtimes{} (\mBbbN{}k {}\mrightarrow{} \mBbbN{})
Date html generated:
2016_05_15-PM-05_25_21
Last ObjectModification:
2015_12_27-PM-02_12_28
Theory : general
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