### Nuprl Lemma : rotate_wf

`∀[k:ℕ]. (rot(k) ∈ ℕk ⟶ ℕk)`

Proof

Definitions occuring in Statement :  rotate: `rot(n)` int_seg: `{i..j-}` nat: `ℕ` uall: `∀[x:A]. B[x]` member: `t ∈ T` function: `x:A ⟶ B[x]` natural_number: `\$n`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` rotate: `rot(n)` nat: `ℕ` int_seg: `{i..j-}` lelt: `i ≤ j < k` and: `P ∧ Q` le: `A ≤ B` less_than': `less_than'(a;b)` false: `False` not: `¬A` implies: `P `` Q` prop: `ℙ` guard: `{T}` ge: `i ≥ j ` all: `∀x:A. B[x]` decidable: `Dec(P)` or: `P ∨ Q` uimplies: `b supposing a` satisfiable_int_formula: `satisfiable_int_formula(fmla)` exists: `∃x:A. B[x]` top: `Top` uiff: `uiff(P;Q)` subtract: `n - m` less_than: `a < b` bool: `𝔹` unit: `Unit` it: `⋅` btrue: `tt` ifthenelse: `if b then t else f fi ` bfalse: `ff` iff: `P `⇐⇒` Q` rev_implies: `P `` Q`
Lemmas referenced :  int_seg_wf nat_wf eq_int_wf subtract_wf bool_wf equal-wf-T-base assert_wf equal_wf false_wf int_seg_properties nat_properties decidable__lt satisfiable-full-omega-tt intformand_wf intformnot_wf intformless_wf itermConstant_wf itermVar_wf intformeq_wf itermSubtract_wf intformle_wf int_formula_prop_and_lemma int_formula_prop_not_lemma int_formula_prop_less_lemma int_term_value_constant_lemma int_term_value_var_lemma int_formula_prop_eq_lemma int_term_value_subtract_lemma int_formula_prop_le_lemma int_formula_prop_wf lelt_wf bnot_wf not_wf add-member-int_seg2 decidable__le uiff_transitivity eqtt_to_assert assert_of_eq_int iff_transitivity iff_weakening_uiff eqff_to_assert assert_of_bnot
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut lambdaEquality extract_by_obid sqequalHypSubstitution isectElimination thin natural_numberEquality setElimination rename hypothesisEquality hypothesis sqequalRule axiomEquality equalityTransitivity equalitySymmetry baseClosed because_Cache intEquality dependent_set_memberEquality independent_pairFormation lambdaFormation productElimination dependent_functionElimination unionElimination independent_isectElimination dependent_pairFormation int_eqEquality isect_memberEquality voidElimination voidEquality computeAll equalityElimination independent_functionElimination impliesFunctionality

Latex:
\mforall{}[k:\mBbbN{}].  (rot(k)  \mmember{}  \mBbbN{}k  {}\mrightarrow{}  \mBbbN{}k)

Date html generated: 2017_04_17-AM-08_04_35
Last ObjectModification: 2017_02_27-PM-04_34_06

Theory : list_1

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