Nuprl Lemma : rotate-by-trivial

`∀[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` nat: `ℕ` le: `A ≤ B` less_than': `less_than'(a;b)` false: `False` not: `¬A` implies: `P `` Q` prop: `ℙ` uiff: `uiff(P;Q)` uimplies: `b supposing a` squash: `↓T` guard: `{T}` all: `∀x:A. B[x]` true: `True` subtype_rel: `A ⊆r B` iff: `P `⇐⇒` Q` rev_implies: `P `` Q`
Lemmas referenced :  rotate-by-id int_seg_wf nat_wf false_wf le_wf equal_wf squash_wf true_wf rotate-by-is-id any_divs_zero iff_weakening_equal less_than_wf divides_reflexivity
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut extract_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality independent_pairFormation hypothesis because_Cache sqequalRule productElimination independent_pairEquality axiomEquality natural_numberEquality setElimination rename isect_memberEquality dependent_set_memberEquality lambdaFormation independent_isectElimination applyEquality lambdaEquality imageElimination equalityTransitivity equalitySymmetry universeEquality intEquality functionEquality dependent_functionElimination imageMemberEquality baseClosed independent_functionElimination hyp_replacement applyLambdaEquality functionExtensionality

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

Date html generated: 2018_05_21-PM-08_18_09
Last ObjectModification: 2017_07_26-PM-05_51_38

Theory : general

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