Nuprl Lemma : baf-bar_wf
∀[R,T:ℕ ⟶ ℕ ⟶ ℙ]. ∀[l:ℕ]. ∀[a:x:ℕl ⟶ ℕ]. (baf-bar(n,m.R[n;m];n,m.T[n;m];l;a) ∈ ℙ)
Proof
Definitions occuring in Statement :
baf-bar: baf-bar(n,m.R[n; m];n,m.T[n; m];l;a),
int_seg: {i..j-},
nat: ℕ,
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s1;s2],
member: t ∈ T,
function: x:A ⟶ B[x],
natural_number: $n
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
baf-bar: baf-bar(n,m.R[n; m];n,m.T[n; m];l;a),
prop: ℙ,
and: P ∧ Q,
subtype_rel: A ⊆r B,
nat: ℕ,
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a,
all: ∀x:A. B[x],
int_seg: {i..j-},
so_apply: x[s1;s2],
lelt: i ≤ j < k,
guard: {T},
ge: i ≥ j ,
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
Lemmas referenced :
lelt_wf,
int_formula_prop_wf,
int_term_value_add_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,
itermAdd_wf,
itermVar_wf,
itermConstant_wf,
intformle_wf,
intformnot_wf,
intformand_wf,
satisfiable-full-omega-tt,
decidable__le,
nat_properties,
int_seg_properties,
exists_wf,
nat_wf,
int_seg_wf,
subtype_rel_dep_function,
strictly-increasing-seq_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
productEquality,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
applyEquality,
natural_numberEquality,
setElimination,
rename,
hypothesis,
lambdaEquality,
because_Cache,
intEquality,
independent_isectElimination,
lambdaFormation,
addEquality,
dependent_set_memberEquality,
productElimination,
independent_pairFormation,
dependent_functionElimination,
unionElimination,
dependent_pairFormation,
int_eqEquality,
isect_memberEquality,
voidElimination,
voidEquality,
computeAll,
universeEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
functionEquality,
cumulativity
Latex:
\mforall{}[R,T:\mBbbN{} {}\mrightarrow{} \mBbbN{} {}\mrightarrow{} \mBbbP{}]. \mforall{}[l:\mBbbN{}]. \mforall{}[a:x:\mBbbN{}l {}\mrightarrow{} \mBbbN{}]. (baf-bar(n,m.R[n;m];n,m.T[n;m];l;a) \mmember{} \mBbbP{})
Date html generated:
2016_05_14-PM-09_51_26
Last ObjectModification:
2016_01_15-PM-10_54_20
Theory : continuity
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