Nuprl Lemma : rotate-by_wf
∀[n,i:ℕ]. (rotate-by(n;i) ∈ ℕn ⟶ ℕn)
Proof
Definitions occuring in Statement :
rotate-by: rotate-by(n;i),
int_seg: {i..j-},
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ⟶ B[x],
natural_number: $n
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
rotate-by: rotate-by(n;i),
int_seg: {i..j-},
nat: ℕ,
nequal: a ≠ b ∈ T ,
guard: {T},
ge: i ≥ j ,
lelt: i ≤ j < k,
and: P ∧ Q,
not: ¬A,
implies: P ⇒ Q,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
all: ∀x:A. B[x],
top: Top,
prop: ℙ,
decidable: Dec(P),
or: P ∨ Q,
nat_plus: ℕ+,
le: A ≤ B
Lemmas referenced :
nat_wf,
int_seg_wf,
lelt_wf,
less_than_wf,
less_than_transitivity2,
le_wf,
int_term_value_add_lemma,
int_formula_prop_not_lemma,
itermAdd_wf,
intformnot_wf,
decidable__le,
rem_bounds_1,
equal_wf,
int_formula_prop_wf,
int_formula_prop_le_lemma,
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,
intformle_wf,
intformless_wf,
itermConstant_wf,
itermVar_wf,
intformeq_wf,
intformand_wf,
satisfiable-full-omega-tt,
nat_properties,
int_seg_properties
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lambdaEquality,
dependent_set_memberEquality,
remainderEquality,
addEquality,
sqequalHypSubstitution,
setElimination,
thin,
rename,
hypothesisEquality,
hypothesis,
because_Cache,
lemma_by_obid,
isectElimination,
productElimination,
lambdaFormation,
natural_numberEquality,
independent_isectElimination,
dependent_pairFormation,
int_eqEquality,
intEquality,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
unionElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[n,i:\mBbbN{}]. (rotate-by(n;i) \mmember{} \mBbbN{}n {}\mrightarrow{} \mBbbN{}n)
Date html generated:
2016_05_15-PM-06_13_43
Last ObjectModification:
2016_01_16-PM-00_47_12
Theory : general
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