Nuprl Lemma : rotate-inverse
∀[n:ℕ+]. (inv(rot(n)) = rot(n)^n - 1 ∈ {f:ℕn ⟶ ℕn| Inj(ℕn;ℕn;f)} )
Proof
Definitions occuring in Statement :
rotate: rot(n),
funinv: inv(f),
fun_exp: f^n,
inject: Inj(A;B;f),
int_seg: {i..j-},
nat_plus: ℕ+,
uall: ∀[x:A]. B[x],
set: {x:A| B[x]} ,
function: x:A ⟶ B[x],
subtract: n - m,
natural_number: $n,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
nat_plus: ℕ+,
prop: ℙ,
nat: ℕ,
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,
squash: ↓T,
true: True,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
funinv-unique,
nat_plus_subtype_nat,
rotate-injection,
rotate_wf,
inject_wf,
int_seg_wf,
fun_exp_wf,
subtract_wf,
nat_plus_properties,
decidable__le,
satisfiable-full-omega-tt,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermSubtract_wf,
itermVar_wf,
intformless_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_subtract_lemma,
int_term_value_var_lemma,
int_formula_prop_less_lemma,
int_formula_prop_wf,
le_wf,
equal_wf,
squash_wf,
true_wf,
rotate-inverse1,
iff_weakening_equal,
nat_plus_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
applyEquality,
hypothesis,
sqequalRule,
because_Cache,
dependent_set_memberEquality,
natural_numberEquality,
setElimination,
rename,
functionExtensionality,
dependent_functionElimination,
unionElimination,
independent_isectElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
imageElimination,
equalityTransitivity,
equalitySymmetry,
universeEquality,
functionEquality,
imageMemberEquality,
baseClosed,
productElimination,
independent_functionElimination
Latex:
\mforall{}[n:\mBbbN{}\msupplus{}]. (inv(rot(n)) = rot(n)\^{}n - 1)
Date html generated:
2017_04_17-AM-08_09_22
Last ObjectModification:
2017_02_27-PM-04_36_12
Theory : list_1
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