Nuprl Lemma : b-almost-full_wf
∀[R:ℕ ⟶ ℕ ⟶ ℙ]. (b-almost-full(n,m.R[n;m]) ∈ ℙ)
Proof
Definitions occuring in Statement :
b-almost-full: b-almost-full(n,m.R[n; m]),
nat: ℕ,
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s1;s2],
member: t ∈ T,
function: x:A ⟶ B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
b-almost-full: b-almost-full(n,m.R[n; m]),
so_lambda: λ2x.t[x],
nat: ℕ,
so_apply: x[s1;s2],
strict-inc: StrictInc,
subtype_rel: A ⊆r B,
guard: {T},
int_upper: {i...},
prop: ℙ,
ge: i ≥ j ,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
implies: P ⇒ Q,
not: ¬A,
top: Top,
and: P ∧ Q,
so_apply: x[s],
so_lambda: λ2x y.t[x; y]
Lemmas referenced :
equiv_rel_true,
true_wf,
int_formula_prop_wf,
int_term_value_var_lemma,
int_term_value_add_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_not_lemma,
int_formula_prop_and_lemma,
itermVar_wf,
itermAdd_wf,
itermConstant_wf,
intformle_wf,
intformnot_wf,
intformand_wf,
satisfiable-full-omega-tt,
decidable__le,
nat_properties,
le_wf,
int_upper_properties,
int_upper_subtype_nat,
int_upper_wf,
nat_wf,
exists_wf,
quotient_wf,
strict-inc_wf,
all_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
lambdaEquality,
addEquality,
setElimination,
rename,
hypothesisEquality,
natural_numberEquality,
applyEquality,
because_Cache,
dependent_set_memberEquality,
setEquality,
intEquality,
dependent_functionElimination,
unionElimination,
independent_isectElimination,
dependent_pairFormation,
int_eqEquality,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
functionEquality,
cumulativity,
universeEquality
Latex:
\mforall{}[R:\mBbbN{} {}\mrightarrow{} \mBbbN{} {}\mrightarrow{} \mBbbP{}]. (b-almost-full(n,m.R[n;m]) \mmember{} \mBbbP{})
Date html generated:
2016_05_14-PM-09_51_07
Last ObjectModification:
2016_01_15-PM-10_55_14
Theory : continuity
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