Nuprl Lemma : fset-subtype
∀[A,B:Type]. fset(A) ⊆r fset(B) supposing A ⊆r B
Proof
Definitions occuring in Statement :
fset: fset(T),
uimplies: b supposing a,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
fset: fset(T),
quotient: x,y:A//B[x; y],
and: P ∧ Q,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
all: ∀x:A. B[x],
guard: {T},
implies: P ⇒ Q,
prop: ℙ,
set-equal: set-equal(T;x;y),
iff: P ⇐⇒ Q,
l_member: (x ∈ l),
exists: ∃x:A. B[x],
cand: A c∧ B,
rev_implies: P ⇐ Q,
nat: ℕ,
ge: i ≥ j ,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
false: False,
not: ¬A,
top: Top,
int_seg: {i..j-},
lelt: i ≤ j < k,
le: A ≤ B,
squash: ↓T,
true: True
Lemmas referenced :
fset_wf,
quotient-member-eq,
list_wf,
set-equal_wf,
set-equal-equiv,
subtype_rel_list,
equal-wf-base,
subtype_rel_wf,
l_member_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,
select_member,
lelt_wf,
length_wf,
equal_wf,
squash_wf,
true_wf,
iff_weakening_equal,
less_than_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaEquality,
sqequalHypSubstitution,
pointwiseFunctionalityForEquality,
extract_by_obid,
isectElimination,
thin,
cumulativity,
hypothesisEquality,
hypothesis,
sqequalRule,
pertypeElimination,
productElimination,
independent_isectElimination,
dependent_functionElimination,
equalityTransitivity,
equalitySymmetry,
applyEquality,
independent_functionElimination,
productEquality,
because_Cache,
axiomEquality,
isect_memberEquality,
universeEquality,
lambdaFormation,
independent_pairFormation,
setElimination,
rename,
natural_numberEquality,
unionElimination,
dependent_pairFormation,
int_eqEquality,
intEquality,
voidElimination,
voidEquality,
computeAll,
dependent_set_memberEquality,
imageElimination,
imageMemberEquality,
baseClosed
Latex:
\mforall{}[A,B:Type]. fset(A) \msubseteq{}r fset(B) supposing A \msubseteq{}r B
Date html generated:
2017_04_17-AM-09_18_47
Last ObjectModification:
2017_02_27-PM-05_22_35
Theory : finite!sets
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