Nuprl Lemma : bsublist_weakening
∀s:DSet. ∀as,bs:|s| List. ((as ≡(|s|) bs) ⇒ (↑bsublist(s;as;bs)))
Proof
Definitions occuring in Statement :
bsublist: bsublist(s;as;bs),
permr: as ≡(T) 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,
guard: {T},
rev_implies: P ⇐ Q,
squash: ↓T,
true: True,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
decidable: Dec(P),
or: P ∨ Q,
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,
itermVar_wf,
intformle_wf,
intformnot_wf,
satisfiable-full-omega-tt,
decidable__le,
iff_weakening_equal,
count_wf,
true_wf,
squash_wf,
le_wf,
count_bsublist,
permr_iff_eq_counts_a,
dset_wf,
list_wf,
set_car_wf,
permr_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
isectElimination,
setElimination,
rename,
hypothesisEquality,
hypothesis,
productElimination,
independent_functionElimination,
because_Cache,
applyEquality,
lambdaEquality,
imageElimination,
equalityTransitivity,
equalitySymmetry,
intEquality,
natural_numberEquality,
sqequalRule,
imageMemberEquality,
baseClosed,
universeEquality,
independent_isectElimination,
unionElimination,
dependent_pairFormation,
int_eqEquality,
isect_memberEquality,
voidElimination,
voidEquality,
computeAll
Latex:
\mforall{}s:DSet. \mforall{}as,bs:|s| List. ((as \mequiv{}(|s|) bs) {}\mRightarrow{} (\muparrow{}bsublist(s;as;bs)))
Date html generated:
2016_05_16-AM-07_41_40
Last ObjectModification:
2016_01_16-PM-11_11_50
Theory : list_2
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