Nuprl Lemma : accum_list_wf
∀[T,A:Type]. ∀[base:T ⟶ A]. ∀[f:A ⟶ T ⟶ A]. ∀[L:T List]. accum_list(a,x.f[a;x];x.base[x];L) ∈ A supposing 0 < ||L||
Proof
Definitions occuring in Statement :
accum_list: accum_list(a,x.f[a; x];x.base[x];L),
length: ||as||,
list: T List,
less_than: a < b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
so_apply: x[s1;s2],
so_apply: x[s],
member: t ∈ T,
function: x:A ⟶ B[x],
natural_number: $n,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
accum_list: accum_list(a,x.f[a; x];x.base[x];L),
so_apply: x[s],
ge: i ≥ j ,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
less_than: a < b,
squash: ↓T,
and: P ∧ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
implies: P ⇒ Q,
not: ¬A,
top: Top,
prop: ℙ,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2]
Lemmas referenced :
list_wf,
less_than_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_not_lemma,
int_formula_prop_and_lemma,
intformless_wf,
itermVar_wf,
itermConstant_wf,
intformle_wf,
intformnot_wf,
intformand_wf,
satisfiable-full-omega-tt,
length_wf,
decidable__le,
hd_wf,
tl_wf,
list_accum_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
cumulativity,
hypothesisEquality,
because_Cache,
hypothesis,
applyEquality,
independent_isectElimination,
dependent_functionElimination,
natural_numberEquality,
unionElimination,
imageElimination,
productElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
functionEquality,
universeEquality
Latex:
\mforall{}[T,A:Type]. \mforall{}[base:T {}\mrightarrow{} A]. \mforall{}[f:A {}\mrightarrow{} T {}\mrightarrow{} A]. \mforall{}[L:T List].
accum\_list(a,x.f[a;x];x.base[x];L) \mmember{} A supposing 0 < ||L||
Date html generated:
2016_05_14-AM-07_39_57
Last ObjectModification:
2016_01_15-AM-08_36_23
Theory : list_1
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