Nuprl Lemma : rotate-order
∀[n:ℕ]. (rot(n)^n = (λx.x) ∈ (ℕn ⟶ ℕn))
Proof
Definitions occuring in Statement :
rotate: rot(n),
fun_exp: f^n,
int_seg: {i..j-},
nat: ℕ,
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,
nat: ℕ,
int_seg: {i..j-},
lelt: i ≤ j < k,
and: P ∧ Q,
le: A ≤ B,
less_than: a < b,
squash: ↓T,
true: True,
prop: ℙ,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
sq_type: SQType(T),
all: ∀x:A. B[x],
ge: i ≥ j ,
decidable: Dec(P),
or: P ∨ Q,
not: ¬A,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
top: Top,
nat_plus: ℕ+,
subtract: n - m
Lemmas referenced :
int_seg_wf,
istype-nat,
equal_wf,
squash_wf,
true_wf,
istype-universe,
iterate-rotate,
subtype_rel_self,
iff_weakening_equal,
subtype_base_sq,
int_subtype_base,
rem_rec_case,
int_seg_properties,
nat_properties,
decidable__le,
full-omega-unsat,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermAdd_wf,
itermVar_wf,
intformless_wf,
istype-int,
int_formula_prop_and_lemma,
istype-void,
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_less_lemma,
int_formula_prop_wf,
istype-le,
decidable__lt,
istype-less_than,
add-associates,
minus-one-mul,
add-swap,
add-commutes,
add-mul-special,
zero-mul,
zero-add,
rem_base_case,
trivial-equal
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
cut,
Error :functionExtensionality_alt,
sqequalRule,
Error :universeIsType,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
natural_numberEquality,
setElimination,
rename,
hypothesisEquality,
hypothesis,
productElimination,
imageElimination,
applyEquality,
Error :lambdaEquality_alt,
equalityTransitivity,
equalitySymmetry,
Error :inhabitedIsType,
instantiate,
universeEquality,
imageMemberEquality,
baseClosed,
because_Cache,
independent_isectElimination,
independent_functionElimination,
cumulativity,
intEquality,
dependent_functionElimination,
Error :dependent_set_memberEquality_alt,
addEquality,
unionElimination,
approximateComputation,
Error :dependent_pairFormation_alt,
int_eqEquality,
Error :isect_memberEquality_alt,
voidElimination,
independent_pairFormation
Latex:
\mforall{}[n:\mBbbN{}]. (rot(n)\^{}n = (\mlambda{}x.x))
Date html generated:
2019_06_20-PM-01_37_13
Last ObjectModification:
2019_03_06-AM-10_51_42
Theory : list_1
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