Nuprl Lemma : is-list-approx_wf
∀T:Type. ∀j:ℕ. (is-list-approx(j) ∈ colist(T) ⟶ partial(𝔹))
Proof
Definitions occuring in Statement :
is-list-approx: is-list-approx(j),
colist: colist(T),
partial: partial(T),
nat: ℕ,
bool: 𝔹,
all: ∀x:A. B[x],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
is-list-approx: is-list-approx(j),
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
member: t ∈ T,
nat: ℕ,
implies: P ⇒ Q,
false: False,
ge: i ≥ j ,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
not: ¬A,
top: Top,
and: P ∧ Q,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
bool: 𝔹,
decidable: Dec(P),
or: P ∨ Q,
nat_plus: ℕ+
Lemmas referenced :
nat_wf,
is-list-fun_wf,
fun_exp_unroll_1,
int_term_value_subtract_lemma,
int_formula_prop_not_lemma,
itermSubtract_wf,
intformnot_wf,
subtract_wf,
decidable__le,
unit_wf2,
union-value-type,
bool_wf,
colist_wf,
bottom_wf_function,
fun_exp0_lemma,
less_than_wf,
ge_wf,
int_formula_prop_wf,
int_formula_prop_less_lemma,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_and_lemma,
intformless_wf,
itermVar_wf,
itermConstant_wf,
intformle_wf,
intformand_wf,
satisfiable-full-omega-tt,
nat_properties
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
setElimination,
rename,
introduction,
intWeakElimination,
natural_numberEquality,
independent_isectElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
independent_functionElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
cumulativity,
because_Cache,
unionElimination,
dependent_set_memberEquality,
applyEquality,
universeEquality
Latex:
\mforall{}T:Type. \mforall{}j:\mBbbN{}. (is-list-approx(j) \mmember{} colist(T) {}\mrightarrow{} partial(\mBbbB{}))
Date html generated:
2016_05_15-PM-10_09_51
Last ObjectModification:
2016_01_11-PM-06_09_24
Theory : eval!all
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