### Nuprl Lemma : rotate-by-is-id

`∀[n,i:ℕ].  rotate-by(n;i) = (λx.x) ∈ (ℕn ⟶ ℕn) supposing n | i`

Proof

Definitions occuring in Statement :  rotate-by: `rotate-by(n;i)` divides: `b | a` int_seg: `{i..j-}` nat: `ℕ` uimplies: `b supposing a` uall: `∀[x:A]. B[x]` lambda: `λx.A[x]` function: `x:A ⟶ B[x]` natural_number: `\$n` equal: `s = t ∈ T`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` uimplies: `b supposing a` uiff: `uiff(P;Q)` and: `P ∧ Q` prop: `ℙ` nat: `ℕ` all: `∀x:A. B[x]` int_nzero: `ℤ-o` nequal: `a ≠ b ∈ T ` ge: `i ≥ j ` not: `¬A` implies: `P `` Q` satisfiable_int_formula: `satisfiable_int_formula(fmla)` exists: `∃x:A. B[x]` false: `False` top: `Top` iff: `P `⇐⇒` Q`
Lemmas referenced :  nequal_wf equal_wf int_formula_prop_wf int_formula_prop_less_lemma int_term_value_constant_lemma int_term_value_var_lemma int_formula_prop_eq_lemma int_formula_prop_and_lemma intformless_wf itermConstant_wf itermVar_wf intformeq_wf intformand_wf satisfiable-full-omega-tt nat_properties divides_iff_rem_zero nat_wf divides_wf less_than_wf rotate-by-id
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut lemma_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality productElimination independent_isectElimination hypothesis natural_numberEquality setElimination rename sqequalRule isect_memberEquality axiomEquality because_Cache equalityTransitivity equalitySymmetry dependent_functionElimination dependent_set_memberEquality lambdaFormation dependent_pairFormation lambdaEquality int_eqEquality intEquality voidElimination voidEquality independent_pairFormation computeAll independent_functionElimination

Latex:
\mforall{}[n,i:\mBbbN{}].    rotate-by(n;i)  =  (\mlambda{}x.x)  supposing  n  |  i

Date html generated: 2016_05_15-PM-06_14_10
Last ObjectModification: 2016_01_16-PM-00_48_33

Theory : general

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