### Nuprl Lemma : rotate-inverse

`∀[n:ℕ+]. (inv(rot(n)) = rot(n)^n - 1 ∈ {f:ℕn ⟶ ℕn| Inj(ℕn;ℕn;f)} )`

Proof

Definitions occuring in Statement :  rotate: `rot(n)` funinv: `inv(f)` fun_exp: `f^n` inject: `Inj(A;B;f)` int_seg: `{i..j-}` nat_plus: `ℕ+` uall: `∀[x:A]. B[x]` set: `{x:A| B[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]` member: `t ∈ T` subtype_rel: `A ⊆r B` nat_plus: `ℕ+` prop: `ℙ` nat: `ℕ` 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` top: `Top` and: `P ∧ Q` squash: `↓T` true: `True` guard: `{T}` iff: `P `⇐⇒` Q` rev_implies: `P `` Q`
Lemmas referenced :  funinv-unique nat_plus_subtype_nat rotate-injection rotate_wf inject_wf int_seg_wf fun_exp_wf subtract_wf 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 equal_wf squash_wf true_wf rotate-inverse1 iff_weakening_equal nat_plus_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation cut introduction extract_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality applyEquality hypothesis sqequalRule because_Cache dependent_set_memberEquality natural_numberEquality setElimination rename functionExtensionality dependent_functionElimination unionElimination independent_isectElimination dependent_pairFormation lambdaEquality int_eqEquality intEquality isect_memberEquality voidElimination voidEquality independent_pairFormation computeAll imageElimination equalityTransitivity equalitySymmetry universeEquality functionEquality imageMemberEquality baseClosed productElimination independent_functionElimination

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

Date html generated: 2017_04_17-AM-08_09_22
Last ObjectModification: 2017_02_27-PM-04_36_12

Theory : list_1

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