### Nuprl Lemma : rotate-inverse1

`∀[n:ℕ+]. ((rot(n) o rot(n)^n - 1) = (λx.x) ∈ (ℕn ⟶ ℕn))`

Proof

Definitions occuring in Statement :  rotate: `rot(n)` fun_exp: `f^n` compose: `f o g` int_seg: `{i..j-}` nat_plus: `ℕ+` uall: `∀[x:A]. B[x]` lambda: `λx.A[x]` function: `x:A ⟶ B[x]` subtract: `n - m` natural_number: `\$n` equal: `s = t ∈ T`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` compose: `f o g` member: `t ∈ T` top: `Top` nat: `ℕ` nat_plus: `ℕ+` guard: `{T}` int_seg: `{i..j-}` lelt: `i ≤ j < k` and: `P ∧ Q` 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]` false: `False` implies: `P `` Q` not: `¬A` prop: `ℙ` true: `True` squash: `↓T` subtype_rel: `A ⊆r B` iff: `P `⇐⇒` Q` rev_implies: `P `` Q`
Lemmas referenced :  fun_exp_add1 subtract_wf int_seg_properties nat_plus_properties decidable__le satisfiable-full-omega-tt intformand_wf intformnot_wf intformle_wf itermConstant_wf itermSubtract_wf itermVar_wf intformless_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_less_lemma int_formula_prop_wf le_wf subtract-add-cancel int_seg_wf nat_plus_wf equal_wf rotate-order iff_weakening_equal
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation cut functionExtensionality sqequalRule introduction extract_by_obid sqequalHypSubstitution isectElimination thin isect_memberEquality voidElimination voidEquality dependent_set_memberEquality setElimination rename hypothesisEquality hypothesis natural_numberEquality because_Cache productElimination dependent_functionElimination unionElimination independent_isectElimination dependent_pairFormation lambdaEquality int_eqEquality intEquality independent_pairFormation computeAll applyEquality imageElimination imageMemberEquality baseClosed equalityTransitivity equalitySymmetry independent_functionElimination

Latex:
\mforall{}[n:\mBbbN{}\msupplus{}].  ((rot(n)  o  rot(n)\^{}n  -  1)  =  (\mlambda{}x.x))

Date html generated: 2017_04_17-AM-08_08_49
Last ObjectModification: 2017_02_27-PM-04_36_20

Theory : list_1

Home Index