Nuprl Lemma : qoset_properties
∀[s:QOSet]. UniformPreorder(|s|;a,b.a ≤ b)
Proof
Definitions occuring in Statement :
qoset: QOSet,
set_leq: a ≤ b,
set_car: |p|,
upreorder: UniformPreorder(T;x,y.R[x; y]),
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
qoset: QOSet,
sq_stable: SqStable(P),
implies: P ⇒ Q,
squash: ↓T,
upreorder: UniformPreorder(T;x,y.R[x; y]),
and: P ∧ Q,
urefl: UniformlyRefl(T;x,y.E[x; y]),
set_leq: a ≤ b,
infix_ap: x f y,
dset: DSet,
utrans: UniformlyTrans(T;x,y.E[x; y]),
prop: ℙ,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2]
Lemmas referenced :
upreorder_wf,
squash_wf,
qoset_wf,
set_leq_wf,
set_car_wf,
set_le_wf,
assert_witness
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
setElimination,
thin,
rename,
independent_functionElimination,
hypothesis,
sqequalRule,
imageMemberEquality,
hypothesisEquality,
baseClosed,
imageElimination,
productElimination,
independent_pairEquality,
isect_memberEquality,
isectElimination,
lemma_by_obid,
applyEquality,
lambdaEquality,
dependent_functionElimination,
lambdaFormation
Latex:
\mforall{}[s:QOSet]. UniformPreorder(|s|;a,b.a \mleq{} b)
Date html generated:
2016_05_15-PM-00_04_32
Last ObjectModification:
2016_01_15-AM-07_08_49
Theory : sets_1
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