Nuprl Lemma : eval-mklist_wf
∀[T:Type]. ∀[n,offset:ℕ]. ∀[f:{offset..n + offset-} ⟶ T]. (eval-mklist(n;f;offset) ∈ T List) supposing value-type(T)
Proof
Definitions occuring in Statement :
eval-mklist: eval-mklist(n;f;offset),
list: T List,
int_seg: {i..j-},
nat: ℕ,
value-type: value-type(T),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ⟶ B[x],
add: n + m,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
int_seg: {i..j-},
nat: ℕ,
ge: i ≥ j ,
lelt: i ≤ j < k,
and: P ∧ Q,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
not: ¬A,
implies: P ⇒ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
top: Top,
prop: ℙ
Lemmas referenced :
eval-mklist-sq,
mklist_wf,
int_seg_properties,
nat_properties,
decidable__le,
full-omega-unsat,
intformand_wf,
intformnot_wf,
intformle_wf,
itermVar_wf,
itermAdd_wf,
itermConstant_wf,
istype-int,
int_formula_prop_and_lemma,
istype-void,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_var_lemma,
int_term_value_add_lemma,
int_term_value_constant_lemma,
int_formula_prop_wf,
decidable__lt,
intformless_wf,
int_formula_prop_less_lemma,
istype-le,
istype-less_than,
int_seg_wf,
istype-nat,
value-type_wf,
istype-universe
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
independent_isectElimination,
hypothesis,
Error :lambdaEquality_alt,
applyEquality,
Error :dependent_set_memberEquality_alt,
addEquality,
setElimination,
rename,
because_Cache,
natural_numberEquality,
productElimination,
independent_pairFormation,
dependent_functionElimination,
unionElimination,
approximateComputation,
independent_functionElimination,
Error :dependent_pairFormation_alt,
int_eqEquality,
Error :isect_memberEquality_alt,
voidElimination,
Error :universeIsType,
Error :productIsType,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
Error :functionIsType,
Error :isectIsTypeImplies,
Error :inhabitedIsType,
instantiate,
universeEquality
Latex:
\mforall{}[T:Type]
\mforall{}[n,offset:\mBbbN{}]. \mforall{}[f:\{offset..n + offset\msupminus{}\} {}\mrightarrow{} T]. (eval-mklist(n;f;offset) \mmember{} T List)
supposing value-type(T)
Date html generated:
2019_06_20-PM-01_31_23
Last ObjectModification:
2019_01_21-AM-11_13_41
Theory : list_1
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