Nuprl Lemma : not-canonicalizable-baire-to-nat

¬⇃(canonicalizable((ℕ ⟶ ℕ) ⟶ ℕ))


Proof




Definitions occuring in Statement :  quotient: x,y:A//B[x; y],  canonicalizable: canonicalizable(T),  nat: ℕ,  not: ¬A,  true: True,  function: x:A ⟶ B[x]
Definitions unfolded in proof :  not: ¬A,  all: ∀x:A. B[x],  member: t ∈ T,  iff: P ⇐⇒ Q,  and: P ∧ Q,  rev_implies: P ⇐ Q,  implies: P ⇒ Q,  uall: ∀[x:A]. B[x],  prop: ℙ,  so_lambda: λ2x y.t[x; y],  so_apply: x[s1;s2],  uimplies: b supposing a,  subtype_rel: A ⊆r B
Lemmas referenced :  choice-principle_wf,  not_wf,  equiv_rel_true,  true_wf,  canonicalizable_wf,  quotient_wf,  nat_wf,  choice-iff-canonicalizable,  not-choice-baire-to-nat
Rules used in proof :  cut,  lemma_by_obid,  hypothesis,  addLevel,  sqequalHypSubstitution,  sqequalSubstitution,  sqequalTransitivity,  computationStep,  sqequalReflexivity,  impliesFunctionality,  dependent_functionElimination,  thin,  functionEquality,  productElimination,  independent_pairFormation,  independent_functionElimination,  isectElimination,  because_Cache,  sqequalRule,  lambdaEquality,  independent_isectElimination,  applyEquality,  cumulativity,  hypothesisEquality,  universeEquality,  instantiate

Latex:
\mneg{}\00D9(canonicalizable((\mBbbN{}  {}\mrightarrow{}  \mBbbN{})  {}\mrightarrow{}  \mBbbN{}))



Date html generated: 2016_05_14-PM-09_42_41
Last ObjectModification: 2016_01_13-AM-10_27_17

Theory : continuity


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