Nuprl Lemma : bdd-val_wf
∀[x:formula()]. ∀[v0:{a:formula()| a ⊆ x ∧ (↑pvar?(a))} ⟶ 𝔹]. ∀[n:ℕ]. (bdd-val(v0;x;n) ∈ Type)
Proof
Definitions occuring in Statement :
bdd-val: bdd-val(v0;x;n),
psub: a ⊆ b,
pvar?: pvar?(v),
formula: formula(),
nat: ℕ,
assert: ↑b,
bool: 𝔹,
uall: ∀[x:A]. B[x],
and: P ∧ Q,
member: t ∈ T,
set: {x:A| B[x]} ,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
bdd-val: bdd-val(v0;x;n),
and: P ∧ Q,
prop: ℙ,
subtype_rel: A ⊆r B,
nat: ℕ,
all: ∀x:A. B[x],
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a,
ge: i ≥ j ,
decidable: Dec(P),
or: P ∨ Q,
le: A ≤ B,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
implies: P ⇒ Q,
not: ¬A,
top: Top,
cand: A c∧ B,
guard: {T}
Lemmas referenced :
ext-eq_weakening,
subtype_rel_weakening,
psub_transitivity,
subtype_rel_sets,
subtype_rel_dep_function,
int_formula_prop_wf,
int_formula_prop_le_lemma,
int_term_value_var_lemma,
int_formula_prop_less_lemma,
int_formula_prop_not_lemma,
int_formula_prop_and_lemma,
intformle_wf,
itermVar_wf,
intformless_wf,
intformnot_wf,
intformand_wf,
satisfiable-full-omega-tt,
decidable__lt,
nat_properties,
prank_functionality,
set_wf,
pvar?_wf,
assert_wf,
nat_wf,
extend-val_wf,
equal_wf,
all_wf,
bool_wf,
and_wf,
prank_wf,
less_than_wf,
psub_wf,
formula_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
setEquality,
functionEquality,
lemma_by_obid,
hypothesis,
productEquality,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
because_Cache,
applyEquality,
setElimination,
rename,
lambdaFormation,
lambdaEquality,
dependent_set_memberEquality,
productElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
independent_isectElimination,
dependent_functionElimination,
unionElimination,
natural_numberEquality,
dependent_pairFormation,
int_eqEquality,
intEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
independent_functionElimination
Latex:
\mforall{}[x:formula()]. \mforall{}[v0:\{a:formula()| a \msubseteq{} x \mwedge{} (\muparrow{}pvar?(a))\} {}\mrightarrow{} \mBbbB{}]. \mforall{}[n:\mBbbN{}]. (bdd-val(v0;x;n) \mmember{} Type)
Date html generated:
2016_05_15-PM-07_16_19
Last ObjectModification:
2016_01_16-AM-09_46_40
Theory : general
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