### Nuprl Lemma : fshift_wf

`∀[n,k:ℕ]. ∀[f:ℕn ⟶ ℕk]. ∀[x:ℕk].  (fshift(f;x) ∈ ℕn + 1 ⟶ ℕk)`

Proof

Definitions occuring in Statement :  fshift: `fshift(f;x)` int_seg: `{i..j-}` nat: `ℕ` uall: `∀[x:A]. B[x]` member: `t ∈ T` function: `x:A ⟶ B[x]` add: `n + m` natural_number: `\$n`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` fshift: `fshift(f;x)` int_seg: `{i..j-}` all: `∀x:A. B[x]` implies: `P `` Q` bool: `𝔹` unit: `Unit` it: `⋅` btrue: `tt` ifthenelse: `if b then t else f fi ` bfalse: `ff` uiff: `uiff(P;Q)` and: `P ∧ Q` uimplies: `b supposing a` exists: `∃x:A. B[x]` prop: `ℙ` or: `P ∨ Q` sq_type: `SQType(T)` guard: `{T}` bnot: `¬bb` assert: `↑b` false: `False` nat: `ℕ` lelt: `i ≤ j < k` nequal: `a ≠ b ∈ T ` ge: `i ≥ j ` decidable: `Dec(P)` not: `¬A` satisfiable_int_formula: `satisfiable_int_formula(fmla)` top: `Top`
Lemmas referenced :  eq_int_wf bool_wf eqff_to_assert equal_wf bool_cases_sqequal subtype_base_sq bool_subtype_base assert-bnot neg_assert_of_eq_int int_seg_wf subtract_wf int_seg_properties nat_properties decidable__le full-omega-unsat intformand_wf intformnot_wf intformle_wf itermConstant_wf itermSubtract_wf itermVar_wf intformeq_wf int_formula_prop_and_lemma int_formula_prop_not_lemma int_formula_prop_le_lemma int_term_value_constant_lemma int_term_value_subtract_lemma int_term_value_var_lemma int_formula_prop_eq_lemma int_formula_prop_wf decidable__lt intformless_wf itermAdd_wf int_formula_prop_less_lemma int_term_value_add_lemma lelt_wf nat_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity Error :isect_memberFormation_alt,  introduction cut sqequalRule lambdaEquality extract_by_obid sqequalHypSubstitution isectElimination thin setElimination rename because_Cache hypothesis natural_numberEquality lambdaFormation unionElimination equalityElimination hypothesisEquality productElimination independent_isectElimination equalityTransitivity equalitySymmetry dependent_pairFormation promote_hyp dependent_functionElimination instantiate cumulativity independent_functionElimination voidElimination applyEquality functionExtensionality dependent_set_memberEquality independent_pairFormation addEquality approximateComputation int_eqEquality intEquality isect_memberEquality voidEquality axiomEquality Error :universeIsType,  Error :functionIsType,  functionEquality Error :inhabitedIsType

Latex:
\mforall{}[n,k:\mBbbN{}].  \mforall{}[f:\mBbbN{}n  {}\mrightarrow{}  \mBbbN{}k].  \mforall{}[x:\mBbbN{}k].    (fshift(f;x)  \mmember{}  \mBbbN{}n  +  1  {}\mrightarrow{}  \mBbbN{}k)

Date html generated: 2019_06_20-PM-02_29_02
Last ObjectModification: 2018_09_26-PM-05_50_54

Theory : num_thy_1

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