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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