Nuprl Lemma : fshift_wf
∀[n,k:ℕ]. ∀[f:ℕn ⟶ ℕk]. ∀[x:ℕk]. (fshift(f;x) ∈ ℕn + 1 ⟶ ℕk)
Proof
Definitions occuring in Statement :
fshift: fshift(f;x),
int_seg: {i..j-},
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ⟶ B[x],
add: n + m,
natural_number: $n
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
fshift: fshift(f;x),
int_seg: {i..j-},
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
ifthenelse: if b then t else f fi ,
bfalse: ff,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
exists: ∃x:A. B[x],
prop: ℙ,
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
false: False,
nat: ℕ,
lelt: i ≤ j < k,
nequal: a ≠ b ∈ T ,
ge: i ≥ j ,
decidable: Dec(P),
not: ¬A,
satisfiable_int_formula: satisfiable_int_formula(fmla),
top: Top
Lemmas referenced :
eq_int_wf,
bool_wf,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_int,
int_seg_wf,
subtract_wf,
int_seg_properties,
nat_properties,
decidable__le,
full-omega-unsat,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermSubtract_wf,
itermVar_wf,
intformeq_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_eq_lemma,
int_formula_prop_wf,
decidable__lt,
intformless_wf,
itermAdd_wf,
int_formula_prop_less_lemma,
int_term_value_add_lemma,
lelt_wf,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
lambdaEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
setElimination,
rename,
because_Cache,
hypothesis,
natural_numberEquality,
lambdaFormation,
unionElimination,
equalityElimination,
hypothesisEquality,
productElimination,
independent_isectElimination,
equalityTransitivity,
equalitySymmetry,
dependent_pairFormation,
promote_hyp,
dependent_functionElimination,
instantiate,
cumulativity,
independent_functionElimination,
voidElimination,
applyEquality,
functionExtensionality,
dependent_set_memberEquality,
independent_pairFormation,
addEquality,
approximateComputation,
int_eqEquality,
intEquality,
isect_memberEquality,
voidEquality,
axiomEquality,
Error :universeIsType,
Error :functionIsType,
functionEquality,
Error :inhabitedIsType
Latex:
\mforall{}[n,k:\mBbbN{}]. \mforall{}[f:\mBbbN{}n {}\mrightarrow{} \mBbbN{}k]. \mforall{}[x:\mBbbN{}k]. (fshift(f;x) \mmember{} \mBbbN{}n + 1 {}\mrightarrow{} \mBbbN{}k)
Date html generated:
2019_06_20-PM-02_29_02
Last ObjectModification:
2018_09_26-PM-05_50_54
Theory : num_thy_1
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