Nuprl Lemma : llex-irreflexive
∀[A:Type]. ∀[<:A ⟶ A ⟶ ℙ]. ((∀a:A. (¬<[a;a])) ⇒ (∀[L:A List]. (¬(L llex(A;a,b.<[a;b]) L))))
Proof
Definitions occuring in Statement :
llex: llex(A;a,b.<[a; b]),
list: T List,
uall: ∀[x:A]. B[x],
prop: ℙ,
infix_ap: x f y,
so_apply: x[s1;s2],
all: ∀x:A. B[x],
not: ¬A,
implies: P ⇒ Q,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
llex: llex(A;a,b.<[a; b]),
infix_ap: x f y,
uall: ∀[x:A]. B[x],
member: t ∈ T,
implies: P ⇒ Q,
not: ¬A,
false: False,
or: P ∨ Q,
and: P ∧ Q,
less_than: a < b,
squash: ↓T,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
all: ∀x:A. B[x],
top: Top,
prop: ℙ,
so_lambda: λ2x.t[x],
int_seg: {i..j-},
guard: {T},
lelt: i ≤ j < k,
so_apply: x[s],
nat: ℕ,
ge: i ≥ j ,
decidable: Dec(P),
so_apply: x[s1;s2],
subtype_rel: A ⊆r B
Lemmas referenced :
not_wf,
list_wf,
decidable__lt,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_not_lemma,
int_formula_prop_and_lemma,
itermConstant_wf,
intformle_wf,
intformnot_wf,
intformand_wf,
decidable__le,
nat_properties,
nat_wf,
exists_wf,
int_seg_properties,
select_wf,
member_wf,
int_seg_wf,
all_wf,
length_wf,
less_than_wf,
or_wf,
int_formula_prop_wf,
int_term_value_var_lemma,
int_formula_prop_less_lemma,
itermVar_wf,
intformless_wf,
satisfiable-full-omega-tt
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
thin,
sqequalHypSubstitution,
unionElimination,
productElimination,
imageElimination,
hypothesis,
lemma_by_obid,
isectElimination,
natural_numberEquality,
independent_isectElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
hypothesisEquality,
intEquality,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
computeAll,
because_Cache,
independent_functionElimination,
productEquality,
cumulativity,
setElimination,
rename,
independent_pairFormation,
applyEquality,
universeEquality,
functionEquality
Latex:
\mforall{}[A:Type]. \mforall{}[<:A {}\mrightarrow{} A {}\mrightarrow{} \mBbbP{}]. ((\mforall{}a:A. (\mneg{}<[a;a])) {}\mRightarrow{} (\mforall{}[L:A List]. (\mneg{}(L llex(A;a,b.<[a;b]) L))))
Date html generated:
2016_05_15-PM-04_18_01
Last ObjectModification:
2016_01_16-AM-11_08_52
Theory : general
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