Nuprl Lemma : rel-path-between_wf
∀[T:Type]. ∀[R:T ⟶ T ⟶ ℙ]. ∀[L:T List]. ∀[x,y:T]. (rel-path-between(T;R;x;y;L) ∈ ℙ)
Proof
Definitions occuring in Statement :
rel-path-between: rel-path-between(T;R;x;y;L),
list: T List,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
rel-path-between: rel-path-between(T;R;x;y;L),
uall: ∀[x:A]. B[x],
member: t ∈ T,
prop: ℙ,
and: P ∧ Q,
uimplies: b supposing a,
ge: i ≥ j ,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
less_than: a < b,
squash: ↓T,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
implies: P ⇒ Q,
not: ¬A,
top: Top,
assert: ↑b,
ifthenelse: if b then t else f fi ,
btrue: tt,
less_than': less_than'(a;b),
cons: [a / b],
bfalse: ff
Lemmas referenced :
rel-path_wf,
less_than_wf,
length_wf,
equal_wf,
hd_wf,
decidable__le,
satisfiable-full-omega-tt,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
intformless_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_less_lemma,
int_formula_prop_wf,
last_wf,
list-cases,
null_nil_lemma,
length_of_nil_lemma,
product_subtype_list,
null_cons_lemma,
length_of_cons_lemma,
false_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
productEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
cumulativity,
hypothesisEquality,
functionExtensionality,
applyEquality,
because_Cache,
hypothesis,
natural_numberEquality,
independent_isectElimination,
dependent_functionElimination,
unionElimination,
imageElimination,
productElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
promote_hyp,
hypothesis_subsumption,
lambdaFormation,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
functionEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[R:T {}\mrightarrow{} T {}\mrightarrow{} \mBbbP{}]. \mforall{}[L:T List]. \mforall{}[x,y:T]. (rel-path-between(T;R;x;y;L) \mmember{} \mBbbP{})
Date html generated:
2017_04_17-AM-09_26_55
Last ObjectModification:
2017_02_27-PM-05_27_45
Theory : relations2
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