Nuprl Lemma : lexico_wf
∀[T:Type]. ∀[lt:T ⟶ T ⟶ ℙ]. (lexico(T; a,b.lt[a;b]) ∈ (T List) ⟶ (T List) ⟶ ℙ)
Proof
Definitions occuring in Statement :
lexico: lexico(T; a,b.lt[a; b]),
list: T List,
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s1;s2],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
lexico: lexico(T; a,b.lt[a; b]),
prop: ℙ,
and: P ∧ Q,
so_lambda: λ2x.t[x],
so_apply: x[s1;s2],
int_seg: {i..j-},
uimplies: b supposing a,
guard: {T},
lelt: i ≤ j < k,
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,
subtype_rel: A ⊆r B,
so_apply: x[s]
Lemmas referenced :
or_wf,
less_than_wf,
length_wf,
equal_wf,
exists_wf,
int_seg_wf,
select_wf,
int_seg_properties,
decidable__le,
satisfiable-full-omega-tt,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_wf,
decidable__lt,
intformless_wf,
int_formula_prop_less_lemma,
intformeq_wf,
int_formula_prop_eq_lemma,
all_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lambdaEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
cumulativity,
hypothesisEquality,
hypothesis,
because_Cache,
productEquality,
intEquality,
natural_numberEquality,
applyEquality,
functionExtensionality,
setElimination,
rename,
independent_isectElimination,
equalityTransitivity,
equalitySymmetry,
productElimination,
dependent_functionElimination,
unionElimination,
dependent_pairFormation,
int_eqEquality,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
axiomEquality,
functionEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[lt:T {}\mrightarrow{} T {}\mrightarrow{} \mBbbP{}]. (lexico(T; a,b.lt[a;b]) \mmember{} (T List) {}\mrightarrow{} (T List) {}\mrightarrow{} \mBbbP{})
Date html generated:
2018_05_21-PM-08_36_52
Last ObjectModification:
2017_07_26-PM-06_01_24
Theory : general
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