Nuprl Lemma : nat-retractible

`retractible(ℕ)`

Proof

Definitions occuring in Statement :  retractible: `retractible(T)` nat: `ℕ`
Definitions unfolded in proof :  retractible: `retractible(T)` exists: `∃x:A. B[x]` member: `t ∈ T` and: `P ∧ Q` all: `∀x:A. B[x]` subtype_rel: `A ⊆r B` nat: `ℕ` uall: `∀[x:A]. B[x]` so_lambda: `λ2x.t[x]` so_apply: `x[s]` uimplies: `b supposing a` implies: `P `` Q` prop: `ℙ` bool: `𝔹` unit: `Unit` it: `⋅` btrue: `tt` uiff: `uiff(P;Q)` 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` has-value: `(a)↓` gt: `i > j`
Lemmas referenced :  nat_wf set_subtype_base le_wf istype-int int_subtype_base has-value_wf_base lt_int_wf eqtt_to_assert assert_of_lt_int top_wf 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 base_wf bottom_diverge not-gt-2
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity Error :dependent_pairFormation_alt,  baseClosed sqequalRule Error :productIsType,  Error :functionIsType,  Error :universeIsType,  cut introduction extract_by_obid hypothesis Error :equalityIsType4,  Error :inhabitedIsType,  hypothesisEquality baseApply closedConclusion applyEquality thin sqequalHypSubstitution isectElimination intEquality Error :lambdaEquality_alt,  natural_numberEquality independent_isectElimination because_Cache independent_pairFormation Error :lambdaFormation_alt,  setElimination rename unionElimination equalityElimination productElimination lessCases Error :isect_memberFormation_alt,  axiomSqEquality Error :isect_memberEquality_alt,  voidElimination imageMemberEquality imageElimination independent_functionElimination equalityTransitivity equalitySymmetry Error :equalityIsType1,  promote_hyp dependent_functionElimination instantiate cumulativity callbyvalueLess Error :equalityIsType2,  Error :dependent_set_memberEquality_alt

Latex:
retractible(\mBbbN{})

Date html generated: 2019_06_20-AM-11_28_24
Last ObjectModification: 2018_09_29-PM-10_53_19

Theory : call!by!value_2

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