Nuprl Lemma : loset_trichot
∀s:LOSet. ∀a,b:|s|. ((a <s b) ∨ (a = b ∈ |s|) ∨ (b <s a))
Proof
Definitions occuring in Statement :
loset: LOSet,
set_lt: a <p b,
set_car: |p|,
all: ∀x:A. B[x],
or: P ∨ Q,
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
loset: LOSet,
poset: POSet{i},
qoset: QOSet,
dset: DSet,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
implies: P ⇒ Q,
iff: P ⇐⇒ Q,
and: P ∧ Q,
guard: {T},
or: P ∨ Q,
uiff: uiff(P;Q),
uimplies: b supposing a,
prop: ℙ,
symmetrize: Symmetrize(x,y.R[x; y];a;b)
Lemmas referenced :
set_car_wf,
loset_wf,
loset_properties,
connex_iff_trichot,
set_leq_wf,
decidable__set_leq,
set_lt_is_sp_of_leq,
or_wf,
equal_wf,
set_lt_wf,
poset_anti_sym
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
setElimination,
rename,
hypothesisEquality,
hypothesis,
dependent_functionElimination,
sqequalRule,
lambdaEquality,
independent_functionElimination,
because_Cache,
productElimination,
unionElimination,
independent_isectElimination,
inlFormation,
inrFormation
Latex:
\mforall{}s:LOSet. \mforall{}a,b:|s|. ((a <s b) \mvee{} (a = b) \mvee{} (b <s a))
Date html generated:
2016_05_15-PM-00_05_31
Last ObjectModification:
2015_12_26-PM-11_27_45
Theory : sets_1
Home
Index