Nuprl Lemma : f-proper-subset-dec_wf
∀[T:Type]. ∀[eq:EqDecider(T)]. ∀[xs,ys:fset(T)]. (f-proper-subset-dec(eq;xs;ys) ∈ 𝔹)
Proof
Definitions occuring in Statement :
f-proper-subset-dec: f-proper-subset-dec(eq;xs;ys),
fset: fset(T),
deq: EqDecider(T),
bool: 𝔹,
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
f-proper-subset-dec: f-proper-subset-dec(eq;xs;ys),
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
iff: P ⇐⇒ Q,
all: ∀x:A. B[x],
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
and: P ∧ Q,
prop: ℙ,
deq: EqDecider(T)
Lemmas referenced :
band_wf,
deq-f-subset_wf,
fset_wf,
bool_wf,
all_wf,
iff_wf,
f-subset_wf,
assert_wf,
bnot_wf,
deq-fset_wf,
deq_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
applyEquality,
hypothesisEquality,
hypothesis,
lambdaEquality,
setElimination,
rename,
setEquality,
functionEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[eq:EqDecider(T)]. \mforall{}[xs,ys:fset(T)]. (f-proper-subset-dec(eq;xs;ys) \mmember{} \mBbbB{})
Date html generated:
2016_05_14-PM-03_41_55
Last ObjectModification:
2015_12_26-PM-06_40_03
Theory : finite!sets
Home
Index