Nuprl Lemma : rotate_wf
∀[k:ℕ]. (rot(k) ∈ ℕk ⟶ ℕk)
Proof
Definitions occuring in Statement :
rotate: rot(n),
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: rot(n),
nat: ℕ,
int_seg: {i..j-},
lelt: i ≤ j < k,
and: P ∧ Q,
le: A ≤ B,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
prop: ℙ,
guard: {T},
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],
top: Top,
uiff: uiff(P;Q),
subtract: n - m,
less_than: a < b,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
ifthenelse: if b then t else f fi ,
bfalse: ff,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
int_seg_wf,
nat_wf,
eq_int_wf,
subtract_wf,
bool_wf,
equal-wf-T-base,
assert_wf,
equal_wf,
false_wf,
int_seg_properties,
nat_properties,
decidable__lt,
satisfiable-full-omega-tt,
intformand_wf,
intformnot_wf,
intformless_wf,
itermConstant_wf,
itermVar_wf,
intformeq_wf,
itermSubtract_wf,
intformle_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_less_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_eq_lemma,
int_term_value_subtract_lemma,
int_formula_prop_le_lemma,
int_formula_prop_wf,
lelt_wf,
bnot_wf,
not_wf,
add-member-int_seg2,
decidable__le,
uiff_transitivity,
eqtt_to_assert,
assert_of_eq_int,
iff_transitivity,
iff_weakening_uiff,
eqff_to_assert,
assert_of_bnot
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
natural_numberEquality,
setElimination,
rename,
hypothesisEquality,
hypothesis,
sqequalRule,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
baseClosed,
because_Cache,
intEquality,
dependent_set_memberEquality,
independent_pairFormation,
lambdaFormation,
productElimination,
dependent_functionElimination,
unionElimination,
independent_isectElimination,
dependent_pairFormation,
int_eqEquality,
isect_memberEquality,
voidElimination,
voidEquality,
computeAll,
equalityElimination,
independent_functionElimination,
impliesFunctionality
Latex:
\mforall{}[k:\mBbbN{}]. (rot(k) \mmember{} \mBbbN{}k {}\mrightarrow{} \mBbbN{}k)
Date html generated:
2017_04_17-AM-08_04_35
Last ObjectModification:
2017_02_27-PM-04_34_06
Theory : list_1
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