### Nuprl Lemma : compose-rotate-by

`∀[n,i,j:ℕ].  ((rotate-by(n;i) o rotate-by(n;j)) = rotate-by(n;i + j) ∈ (ℕn ⟶ ℕn))`

Proof

Definitions occuring in Statement :  rotate-by: `rotate-by(n;i)` compose: `f o g` int_seg: `{i..j-}` nat: `ℕ` uall: `∀[x:A]. B[x]` function: `x:A ⟶ B[x]` add: `n + m` natural_number: `\$n` equal: `s = t ∈ T`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` nat: `ℕ` true: `True` 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]` false: `False` implies: `P `` Q` not: `¬A` top: `Top` and: `P ∧ Q` prop: `ℙ` squash: `↓T` subtype_rel: `A ⊆r B` guard: `{T}` iff: `P `⇐⇒` Q` rev_implies: `P `` Q`
Lemmas referenced :  nat_wf int_seg_wf nat_properties decidable__le satisfiable-full-omega-tt intformand_wf intformnot_wf intformle_wf itermConstant_wf itermAdd_wf itermVar_wf int_formula_prop_and_lemma int_formula_prop_not_lemma int_formula_prop_le_lemma int_term_value_constant_lemma int_term_value_add_lemma int_term_value_var_lemma int_formula_prop_wf le_wf equal_wf compose_wf fun_exp_wf rotate_wf fun_exp_add iff_weakening_equal squash_wf true_wf iterate-rotate-rotate-by
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut hypothesis extract_by_obid sqequalRule sqequalHypSubstitution isect_memberEquality isectElimination thin hypothesisEquality axiomEquality because_Cache functionEquality natural_numberEquality setElimination rename dependent_set_memberEquality addEquality dependent_functionElimination unionElimination independent_isectElimination dependent_pairFormation lambdaEquality int_eqEquality intEquality voidElimination voidEquality independent_pairFormation computeAll applyEquality imageElimination imageMemberEquality baseClosed equalityTransitivity equalitySymmetry productElimination independent_functionElimination universeEquality cumulativity

Latex:
\mforall{}[n,i,j:\mBbbN{}].    ((rotate-by(n;i)  o  rotate-by(n;j))  =  rotate-by(n;i  +  j))

Date html generated: 2018_05_21-PM-08_18_35
Last ObjectModification: 2017_07_26-PM-05_52_04

Theory : general

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