Nuprl Lemma : strong-subtype-bag
∀[A,B:Type]. strong-subtype(bag(A);bag(B)) supposing strong-subtype(A;B)
Proof
Definitions occuring in Statement :
bag: bag(T),
strong-subtype: strong-subtype(A;B),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
strong-subtype: strong-subtype(A;B),
cand: A c∧ B,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
exists: ∃x:A. B[x],
prop: ℙ,
implies: P ⇒ Q,
all: ∀x:A. B[x],
bag-member: x ↓∈ bs,
squash: ↓T,
and: P ∧ Q,
sq_stable: SqStable(P),
bag: bag(T),
quotient: x,y:A//B[x; y],
guard: {T},
iff: P ⇐⇒ Q,
l_member: (x ∈ l),
nat: ℕ,
ge: i ≥ j ,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
false: False,
not: ¬A,
top: Top
Lemmas referenced :
subtype_rel_bag,
bag_wf,
exists_wf,
equal_wf,
strong-subtype_witness,
strong-subtype_wf,
bag-subtype,
bag-member_wf,
bag_to_squash_list,
sq_stable__all,
l_member_wf,
list-subtype-bag,
squash_wf,
sq_stable__squash,
member-permutation,
member_wf,
list_wf,
subtype_rel_list,
permutation_wf,
select_wf,
nat_properties,
decidable__le,
satisfiable-full-omega-tt,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermVar_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_wf,
strong-subtype-implies
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
independent_isectElimination,
hypothesis,
productElimination,
independent_pairFormation,
lambdaEquality,
setEquality,
cumulativity,
sqequalRule,
applyEquality,
because_Cache,
independent_functionElimination,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry,
universeEquality,
dependent_functionElimination,
setElimination,
rename,
imageElimination,
functionEquality,
lambdaFormation,
imageMemberEquality,
baseClosed,
promote_hyp,
hyp_replacement,
applyLambdaEquality,
pertypeElimination,
productEquality,
dependent_pairFormation,
natural_numberEquality,
unionElimination,
int_eqEquality,
intEquality,
voidElimination,
voidEquality,
computeAll
Latex:
\mforall{}[A,B:Type]. strong-subtype(bag(A);bag(B)) supposing strong-subtype(A;B)
Date html generated:
2017_10_01-AM-08_56_47
Last ObjectModification:
2017_07_26-PM-04_39_03
Theory : bags
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