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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