Nuprl Lemma : quick-find_wf
∀[n:ℕ+]. ∀[p:{n...} ⟶ 𝔹]. quick-find(p;n) ∈ {m:{n...}| ↑(p m)} supposing ∃N:{n...}. ∀m:{N...}. (↑(p m))
Proof
Definitions occuring in Statement :
quick-find: quick-find(p;n),
int_upper: {i...},
nat_plus: ℕ+,
assert: ↑b,
bool: 𝔹,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
member: t ∈ T,
set: {x:A| B[x]} ,
apply: f a,
function: x:A ⟶ B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
exists: ∃x:A. B[x],
prop: ℙ,
nat_plus: ℕ+,
so_lambda: λ2x.t[x],
int_upper: {i...},
subtype_rel: A ⊆r B,
guard: {T},
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
false: False,
implies: P ⇒ Q,
not: ¬A,
top: Top,
and: P ∧ Q,
so_apply: x[s],
nat: ℕ,
ge: i ≥ j ,
quick-find: quick-find(p;n),
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
bfalse: ff,
sq_type: SQType(T),
bnot: ¬bb,
assert: ↑b,
has-value: (a)↓
Lemmas referenced :
exists_wf,
int_upper_wf,
all_wf,
assert_wf,
int_upper_subtype_int_upper,
int_upper_properties,
nat_plus_properties,
decidable__le,
satisfiable-full-omega-tt,
intformand_wf,
intformnot_wf,
intformle_wf,
itermVar_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_var_lemma,
int_formula_prop_wf,
bool_wf,
nat_plus_wf,
nat_properties,
itermConstant_wf,
intformless_wf,
int_term_value_constant_lemma,
int_formula_prop_less_lemma,
ge_wf,
less_than_wf,
le_wf,
subtract_wf,
itermSubtract_wf,
int_term_value_subtract_lemma,
nat_wf,
itermAdd_wf,
int_term_value_add_lemma,
eqtt_to_assert,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
value-type-has-value,
int-value-type,
itermMultiply_wf,
int_term_value_mul_lemma
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
productElimination,
thin,
hypothesis,
sqequalRule,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
extract_by_obid,
isectElimination,
setElimination,
rename,
because_Cache,
lambdaEquality,
applyEquality,
functionExtensionality,
hypothesisEquality,
independent_isectElimination,
applyLambdaEquality,
dependent_functionElimination,
unionElimination,
natural_numberEquality,
dependent_pairFormation,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
functionEquality,
lambdaFormation,
intWeakElimination,
independent_functionElimination,
addEquality,
dependent_set_memberEquality,
equalityElimination,
promote_hyp,
instantiate,
cumulativity,
callbyvalueReduce,
multiplyEquality
Latex:
\mforall{}[n:\mBbbN{}\msupplus{}]. \mforall{}[p:\{n...\} {}\mrightarrow{} \mBbbB{}]. quick-find(p;n) \mmember{} \{m:\{n...\}| \muparrow{}(p m)\} supposing \mexists{}N:\{n...\}. \mforall{}m:\{N...\}. (\muparrow{}\000C(p m))
Date html generated:
2017_10_01-AM-09_15_24
Last ObjectModification:
2017_07_26-PM-04_50_09
Theory : general
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