### Nuprl Lemma : canonicalizable-baire-direct

`canonicalizable(ℕ ⟶ ℕ)`

Proof

Definitions occuring in Statement :  canonicalizable: `canonicalizable(T)` nat: `ℕ` function: `x:A ⟶ B[x]`
Definitions unfolded in proof :  canonicalizable: `canonicalizable(T)` exists: `∃x:A. B[x]` member: `t ∈ T` all: `∀x:A. B[x]` uall: `∀[x:A]. B[x]` nat: `ℕ` implies: `P `` Q` bool: `𝔹` unit: `Unit` it: `⋅` btrue: `tt` uiff: `uiff(P;Q)` and: `P ∧ Q` uimplies: `b supposing a` less_than: `a < b` less_than': `less_than'(a;b)` top: `Top` true: `True` squash: `↓T` not: `¬A` false: `False` guard: `{T}` bfalse: `ff` or: `P ∨ Q` sq_type: `SQType(T)` bnot: `¬bb` ifthenelse: `if b then t else f fi ` assert: `↑b` iff: `P `⇐⇒` Q` rev_implies: `P `` Q` prop: `ℙ` has-value: `(a)↓` gt: `i > j` so_lambda: `λ2x.t[x]` so_apply: `x[s]`
Lemmas referenced :  lt_int_wf eqtt_to_assert assert_of_lt_int istype-top istype-void less_than_transitivity1 less_than_irreflexivity eqff_to_assert bool_cases_sqequal subtype_base_sq bool_wf bool_subtype_base iff_transitivity assert_wf bnot_wf not_wf less_than_wf iff_weakening_uiff assert_of_bnot nat_wf base_wf bottom-sqle not-gt-2 le_wf set_subtype_base int_subtype_base has-value_wf_base is-exception_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity Error :dependent_pairFormation_alt,  sqequalRule Error :lambdaFormation_alt,  cut Error :functionExtensionality_alt,  introduction extract_by_obid sqequalHypSubstitution isectElimination thin setElimination rename hypothesisEquality hypothesis natural_numberEquality Error :inhabitedIsType,  unionElimination equalityElimination because_Cache productElimination independent_isectElimination lessCases Error :isect_memberFormation_alt,  axiomSqEquality Error :isect_memberEquality_alt,  independent_pairFormation voidElimination imageMemberEquality baseClosed imageElimination independent_functionElimination equalityTransitivity equalitySymmetry Error :equalityIsType1,  promote_hyp dependent_functionElimination instantiate cumulativity Error :universeIsType,  applyEquality Error :functionIsType,  Error :equalityIsType2,  Error :lambdaEquality_alt,  pointwiseFunctionalityForEquality baseApply closedConclusion sqequalSqle divergentSqle callbyvalueLess applyLambdaEquality functionExtensionality Error :dependent_set_memberEquality_alt,  intEquality sqleReflexivity lessExceptionCases axiomSqleEquality exceptionSqequal

Latex:
canonicalizable(\mBbbN{}  {}\mrightarrow{}  \mBbbN{})

Date html generated: 2019_06_20-AM-11_28_29
Last ObjectModification: 2018_09_29-PM-11_05_10

Theory : call!by!value_2

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