Nuprl Lemma : rotate-injection
∀[n:ℕ]. Inj(ℕn;ℕn;rot(n))
Proof
Definitions occuring in Statement :
rotate: rot(n),
inject: Inj(A;B;f),
int_seg: {i..j-},
nat: ℕ,
uall: ∀[x:A]. B[x],
natural_number: $n
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
inject: Inj(A;B;f),
all: ∀x:A. B[x],
implies: P ⇒ Q,
rotate: rot(n),
prop: ℙ,
nat: ℕ,
int_seg: {i..j-},
guard: {T},
lelt: i ≤ j < k,
and: P ∧ Q,
ge: i ≥ j ,
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A,
top: Top,
sq_type: SQType(T),
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
btrue: tt,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
bfalse: ff
Lemmas referenced :
equal_wf,
int_seg_wf,
rotate_wf,
nat_wf,
eq_int_wf,
subtract_wf,
int_seg_properties,
nat_properties,
decidable__equal_int,
satisfiable-full-omega-tt,
intformand_wf,
intformnot_wf,
intformeq_wf,
itermVar_wf,
itermSubtract_wf,
itermConstant_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_eq_lemma,
int_term_value_var_lemma,
int_term_value_subtract_lemma,
int_term_value_constant_lemma,
int_formula_prop_wf,
decidable__le,
intformle_wf,
intformless_wf,
int_formula_prop_le_lemma,
int_formula_prop_less_lemma,
decidable__lt,
lelt_wf,
assert_wf,
bnot_wf,
not_wf,
itermAdd_wf,
int_term_value_add_lemma,
bool_cases,
subtype_base_sq,
bool_wf,
bool_subtype_base,
eqtt_to_assert,
assert_of_eq_int,
eqff_to_assert,
iff_transitivity,
iff_weakening_uiff,
assert_of_bnot
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
sqequalHypSubstitution,
sqequalRule,
hypothesis,
extract_by_obid,
isectElimination,
thin,
natural_numberEquality,
setElimination,
rename,
hypothesisEquality,
applyEquality,
lambdaEquality,
dependent_functionElimination,
axiomEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
applyLambdaEquality,
productElimination,
unionElimination,
independent_isectElimination,
dependent_pairFormation,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
dependent_set_memberEquality,
instantiate,
cumulativity,
independent_functionElimination,
impliesFunctionality
Latex:
\mforall{}[n:\mBbbN{}]. Inj(\mBbbN{}n;\mBbbN{}n;rot(n))
Date html generated:
2017_04_17-AM-08_08_10
Last ObjectModification:
2017_02_27-PM-04_35_55
Theory : list_1
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