Nuprl Lemma : decidable__f-proper-subset
∀[T:Type]. ∀eq:EqDecider(T). ∀xs,ys:fset(T). Dec(xs ⊆≠ ys)
Proof
Definitions occuring in Statement :
f-proper-subset: xs ⊆≠ ys,
fset: fset(T),
deq: EqDecider(T),
decidable: Dec(P),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
member: t ∈ T,
implies: P ⇒ Q,
uiff: uiff(P;Q),
and: P ∧ Q,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
fset_wf,
deq_wf,
f-proper-subset_wf,
assert_wf,
f-proper-subset-dec_wf,
decidable__assert,
decidable_functionality,
iff_weakening_uiff,
assert-f-proper-subset-dec
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
universeEquality,
dependent_functionElimination,
independent_functionElimination,
productElimination,
independent_pairFormation
Latex:
\mforall{}[T:Type]. \mforall{}eq:EqDecider(T). \mforall{}xs,ys:fset(T). Dec(xs \msubseteq{}\mneq{} ys)
Date html generated:
2016_05_14-PM-03_42_01
Last ObjectModification:
2015_12_26-PM-06_40_00
Theory : finite!sets
Home
Index