Nuprl Lemma : rotate-by-is-id
∀[n,i:ℕ]. rotate-by(n;i) = (λx.x) ∈ (ℕn ⟶ ℕn) supposing n | i
Proof
Definitions occuring in Statement :
rotate-by: rotate-by(n;i),
divides: b | a,
int_seg: {i..j-},
nat: ℕ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
lambda: λx.A[x],
function: x:A ⟶ B[x],
natural_number: $n,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
uiff: uiff(P;Q),
and: P ∧ Q,
prop: ℙ,
nat: ℕ,
all: ∀x:A. B[x],
int_nzero: ℤ-o,
nequal: a ≠ b ∈ T ,
ge: i ≥ j ,
not: ¬A,
implies: P ⇒ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
top: Top,
iff: P ⇐⇒ Q
Lemmas referenced :
nequal_wf,
equal_wf,
int_formula_prop_wf,
int_formula_prop_less_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_eq_lemma,
int_formula_prop_and_lemma,
intformless_wf,
itermConstant_wf,
itermVar_wf,
intformeq_wf,
intformand_wf,
satisfiable-full-omega-tt,
nat_properties,
divides_iff_rem_zero,
nat_wf,
divides_wf,
less_than_wf,
rotate-by-id
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
productElimination,
independent_isectElimination,
hypothesis,
natural_numberEquality,
setElimination,
rename,
sqequalRule,
isect_memberEquality,
axiomEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
dependent_set_memberEquality,
lambdaFormation,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
independent_functionElimination
Latex:
\mforall{}[n,i:\mBbbN{}]. rotate-by(n;i) = (\mlambda{}x.x) supposing n | i
Date html generated:
2016_05_15-PM-06_14_10
Last ObjectModification:
2016_01_16-PM-00_48_33
Theory : general
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