Nuprl Lemma : fset-ac-le_weakening_f-subset
∀[T:Type]. ∀[eq:EqDecider(T)]. ∀[a,b:fset(fset(T))]. fset-ac-le(eq;a;b) supposing a ⊆ b
Proof
Definitions occuring in Statement :
fset-ac-le: fset-ac-le(eq;ac1;ac2),
deq-fset: deq-fset(eq),
f-subset: xs ⊆ ys,
fset: fset(T),
deq: EqDecider(T),
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,
fset-ac-le: fset-ac-le(eq;ac1;ac2),
fset-all: fset-all(s;x.P[x]),
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
so_apply: x[s],
iff: P ⇐⇒ Q,
all: ∀x:A. B[x],
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
and: P ∧ Q,
prop: ℙ,
uiff: uiff(P;Q),
rev_uimplies: rev_uimplies(P;Q),
not: ¬A,
guard: {T},
cand: A c∧ B,
f-subset: xs ⊆ ys,
top: Top,
false: False
Lemmas referenced :
assert_witness,
fset-null_wf,
fset_wf,
fset-filter_wf,
bnot_wf,
deq-f-subset_wf,
bool_wf,
all_wf,
iff_wf,
f-subset_wf,
assert_wf,
deq-fset_wf,
deq_wf,
fset-all-iff,
assert_of_bnot,
equal-wf-T-base,
assert-fset-null,
not_wf,
fset-member_wf,
member-fset-filter,
assert-deq-f-subset,
f-subset_weakening,
mem_empty_lemma
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
sqequalHypSubstitution,
extract_by_obid,
isectElimination,
thin,
cumulativity,
hypothesisEquality,
hypothesis,
lambdaEquality,
applyEquality,
setElimination,
rename,
setEquality,
functionEquality,
functionExtensionality,
independent_functionElimination,
isect_memberEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
universeEquality,
productElimination,
independent_isectElimination,
lambdaFormation,
baseClosed,
addLevel,
impliesFunctionality,
independent_pairFormation,
dependent_functionElimination,
hyp_replacement,
Error :applyLambdaEquality,
voidElimination,
voidEquality
Latex:
\mforall{}[T:Type]. \mforall{}[eq:EqDecider(T)]. \mforall{}[a,b:fset(fset(T))]. fset-ac-le(eq;a;b) supposing a \msubseteq{} b
Date html generated:
2016_10_21-AM-10_44_51
Last ObjectModification:
2016_07_12-AM-05_51_49
Theory : finite!sets
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