### Nuprl Lemma : rotate-by-trivial-test

`∀[n:ℕ]. ∀[x:ℕn].  (((rotate-by(n;0) x) = x ∈ ℕn) ∧ ((rotate-by(n;n) x) = x ∈ ℕn))`

Proof

Definitions occuring in Statement :  rotate-by: `rotate-by(n;i)` int_seg: `{i..j-}` nat: `ℕ` uall: `∀[x:A]. B[x]` and: `P ∧ Q` apply: `f a` natural_number: `\$n` equal: `s = t ∈ T`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` and: `P ∧ Q` cand: `A c∧ B` lelt: `i ≤ j < k` guard: `{T}` nat: `ℕ` int_seg: `{i..j-}` ge: `i ≥ j ` all: `∀x:A. B[x]` prop: `ℙ` le: `A ≤ B` less_than': `less_than'(a;b)` false: `False` not: `¬A` implies: `P `` Q` subtype_rel: `A ⊆r B` decidable: `Dec(P)` or: `P ∨ Q` uimplies: `b supposing a` satisfiable_int_formula: `satisfiable_int_formula(fmla)` exists: `∃x:A. B[x]` top: `Top`
Lemmas referenced :  nat_wf int_seg_wf rotate-by-trivial int_formula_prop_less_lemma intformless_wf decidable__lt int_formula_prop_wf int_formula_prop_not_lemma int_term_value_var_lemma int_term_value_constant_lemma int_formula_prop_le_lemma int_formula_prop_and_lemma intformnot_wf itermVar_wf itermConstant_wf intformle_wf intformand_wf satisfiable-full-omega-tt lelt_wf false_wf le_wf rotate-by_wf decidable__le nat_properties int_seg_properties
Rules used in proof :  comment sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut independent_pairFormation lemma_by_obid sqequalHypSubstitution isectElimination thin natural_numberEquality setElimination rename hypothesisEquality hypothesis productElimination dependent_functionElimination applyEquality dependent_set_memberEquality because_Cache sqequalRule lambdaFormation unionElimination equalityTransitivity equalitySymmetry lambdaEquality setEquality intEquality independent_isectElimination dependent_pairFormation int_eqEquality isect_memberEquality voidElimination voidEquality computeAll independent_pairEquality axiomEquality

Latex:
\mforall{}[n:\mBbbN{}].  \mforall{}[x:\mBbbN{}n].    (((rotate-by(n;0)  x)  =  x)  \mwedge{}  ((rotate-by(n;n)  x)  =  x))

Date html generated: 2016_05_15-PM-06_14_46
Last ObjectModification: 2016_01_16-PM-00_48_48

Theory : general

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