Nuprl Lemma : bsublist_transitivity
∀s:DSet. ∀us,vs,ws:|s| List. ((↑bsublist(s;us;vs)) ⇒ (↑bsublist(s;vs;ws)) ⇒ (↑bsublist(s;us;ws)))
Proof
Definitions occuring in Statement :
bsublist: bsublist(s;as;bs),
list: T List,
assert: ↑b,
all: ∀x:A. B[x],
implies: P ⇒ Q,
dset: DSet,
set_car: |p|
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
prop: ℙ,
uall: ∀[x:A]. B[x],
dset: DSet,
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
decidable: Dec(P),
or: P ∨ Q,
le: A ≤ B,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A,
top: Top
Lemmas referenced :
int_formula_prop_wf,
int_term_value_var_lemma,
int_formula_prop_le_lemma,
int_formula_prop_not_lemma,
int_formula_prop_and_lemma,
itermVar_wf,
intformle_wf,
intformnot_wf,
intformand_wf,
satisfiable-full-omega-tt,
count_wf,
decidable__le,
count_bsublist_a,
dset_wf,
set_car_wf,
list_wf,
bsublist_wf,
assert_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
dependent_functionElimination,
hypothesisEquality,
hypothesis,
setElimination,
rename,
productElimination,
independent_functionElimination,
unionElimination,
natural_numberEquality,
independent_isectElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
sqequalRule,
independent_pairFormation,
computeAll
Latex:
\mforall{}s:DSet. \mforall{}us,vs,ws:|s| List. ((\muparrow{}bsublist(s;us;vs)) {}\mRightarrow{} (\muparrow{}bsublist(s;vs;ws)) {}\mRightarrow{} (\muparrow{}bsublist(s;us;ws)))
Date html generated:
2016_05_16-AM-07_41_43
Last ObjectModification:
2016_01_16-PM-11_11_57
Theory : list_2
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