Nuprl Lemma : rotate-by-trivial-test
∀[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,
lelt: i ≤ j < k,
guard: {T},
nat: ℕ,
int_seg: {i..j-},
ge: i ≥ j ,
all: ∀x:A. B[x],
prop: ℙ,
le: A ≤ B,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
subtype_rel: A ⊆r B,
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
top: Top
Lemmas referenced :
nat_wf,
int_seg_wf,
rotate-by-trivial,
int_formula_prop_less_lemma,
intformless_wf,
decidable__lt,
int_formula_prop_wf,
int_formula_prop_not_lemma,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_and_lemma,
intformnot_wf,
itermVar_wf,
itermConstant_wf,
intformle_wf,
intformand_wf,
satisfiable-full-omega-tt,
lelt_wf,
false_wf,
le_wf,
rotate-by_wf,
decidable__le,
nat_properties,
int_seg_properties
Rules used in proof :
comment,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
independent_pairFormation,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
natural_numberEquality,
setElimination,
rename,
hypothesisEquality,
hypothesis,
productElimination,
dependent_functionElimination,
applyEquality,
dependent_set_memberEquality,
because_Cache,
sqequalRule,
lambdaFormation,
unionElimination,
equalityTransitivity,
equalitySymmetry,
lambdaEquality,
setEquality,
intEquality,
independent_isectElimination,
dependent_pairFormation,
int_eqEquality,
isect_memberEquality,
voidElimination,
voidEquality,
computeAll,
independent_pairEquality,
axiomEquality
Latex:
\mforall{}[n:\mBbbN{}]. \mforall{}[x:\mBbbN{}n]. (((rotate-by(n;0) x) = x) \mwedge{} ((rotate-by(n;n) x) = x))
Date html generated:
2016_05_15-PM-06_14_46
Last ObjectModification:
2016_01_16-PM-00_48_48
Theory : general
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