Nuprl Lemma : bag-drop-head
∀[T:Type]. ∀[eq:EqDecider(T)]. ∀[bs:bag(T)]. ∀[x:T]. (bag-drop(eq;[x / bs];x) ~ bs)
Proof
Definitions occuring in Statement :
bag-drop: bag-drop(eq;bs;a),
bag: bag(T),
cons: [a / b],
deq: EqDecider(T),
uall: ∀[x:A]. B[x],
universe: Type,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
bag-drop: bag-drop(eq;bs;a),
bag-remove1: bag-remove1(eq;bs;a),
bag_remove1_aux: bag_remove1_aux(eq;checked;a;as),
all: ∀x:A. B[x],
so_lambda: so_lambda(x,y,z.t[x; y; z]),
top: Top,
so_apply: x[s1;s2;s3],
append: as @ bs,
deq: EqDecider(T),
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
eqof: eqof(d),
ifthenelse: if b then t else f fi ,
bfalse: ff,
exists: ∃x:A. B[x],
prop: ℙ,
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
false: False,
not: ¬A
Lemmas referenced :
bag_wf,
deq_wf,
list_ind_cons_lemma,
list_ind_nil_lemma,
bool_wf,
eqtt_to_assert,
safe-assert-deq,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
hypothesis,
sqequalAxiom,
hypothesisEquality,
sqequalHypSubstitution,
isect_memberEquality,
isectElimination,
thin,
because_Cache,
extract_by_obid,
cumulativity,
universeEquality,
dependent_functionElimination,
voidElimination,
voidEquality,
applyEquality,
setElimination,
rename,
lambdaFormation,
unionElimination,
equalityElimination,
equalityTransitivity,
equalitySymmetry,
productElimination,
independent_isectElimination,
dependent_pairFormation,
promote_hyp,
instantiate,
independent_functionElimination
Latex:
\mforall{}[T:Type]. \mforall{}[eq:EqDecider(T)]. \mforall{}[bs:bag(T)]. \mforall{}[x:T]. (bag-drop(eq;[x / bs];x) \msim{} bs)
Date html generated:
2018_05_21-PM-09_48_50
Last ObjectModification:
2017_07_26-PM-06_30_46
Theory : bags_2
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