Nuprl Lemma : l_all_wf2
∀[T:Type]. ∀[L:T List]. ∀[P:{x:T| (x ∈ L)} ⟶ ℙ]. ((∀x∈L.P[x]) ∈ ℙ)
Proof
Definitions occuring in Statement :
l_all: (∀x∈L.P[x]),
l_member: (x ∈ l),
list: T List,
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s],
member: t ∈ T,
set: {x:A| B[x]} ,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
l_all: (∀x∈L.P[x]),
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
so_apply: x[s],
prop: ℙ,
uimplies: b supposing a,
guard: {T},
int_seg: {i..j-},
lelt: i ≤ j < k,
and: P ∧ Q,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
implies: P ⇒ Q,
not: ¬A,
top: Top,
less_than: a < b,
squash: ↓T
Lemmas referenced :
list_wf,
int_formula_prop_less_lemma,
intformless_wf,
decidable__lt,
int_formula_prop_wf,
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,
itermVar_wf,
itermConstant_wf,
intformle_wf,
intformnot_wf,
intformand_wf,
satisfiable-full-omega-tt,
decidable__le,
int_seg_properties,
list-subtype,
l_member_wf,
select_wf,
length_wf,
int_seg_wf,
all_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
natural_numberEquality,
cumulativity,
hypothesisEquality,
hypothesis,
lambdaEquality,
applyEquality,
setEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
independent_isectElimination,
setElimination,
rename,
productElimination,
dependent_functionElimination,
unionElimination,
dependent_pairFormation,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
imageElimination,
axiomEquality,
functionEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[L:T List]. \mforall{}[P:\{x:T| (x \mmember{} L)\} {}\mrightarrow{} \mBbbP{}]. ((\mforall{}x\mmember{}L.P[x]) \mmember{} \mBbbP{})
Date html generated:
2016_05_15-PM-03_38_07
Last ObjectModification:
2016_01_16-AM-10_51_18
Theory : general
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