Nuprl Lemma : set_leq_transitivity
∀[s:QOSet]. ∀[a,b,c:|s|]. (a ≤ c) supposing ((b ≤ c) and (a ≤ b))
Proof
Definitions occuring in Statement :
qoset: QOSet,
set_leq: a ≤ b,
set_car: |p|,
uimplies: b supposing a,
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
upreorder: UniformPreorder(T;x,y.R[x; y]),
and: P ∧ Q,
utrans: UniformlyTrans(T;x,y.E[x; y]),
urefl: UniformlyRefl(T;x,y.E[x; y]),
implies: P ⇒ Q,
set_leq: a ≤ b,
infix_ap: x f y,
qoset: QOSet,
dset: DSet,
prop: ℙ,
uimplies: b supposing a,
guard: {T}
Lemmas referenced :
qoset_properties,
assert_witness,
set_le_wf,
set_leq_wf,
set_car_wf,
qoset_wf
Rules used in proof :
cut,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
productElimination,
sqequalRule,
isect_memberEquality,
lambdaEquality,
dependent_functionElimination,
applyEquality,
setElimination,
rename,
independent_functionElimination,
because_Cache,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[s:QOSet]. \mforall{}[a,b,c:|s|]. (a \mleq{} c) supposing ((b \mleq{} c) and (a \mleq{} b))
Date html generated:
2016_05_15-PM-00_04_40
Last ObjectModification:
2015_12_26-PM-11_28_21
Theory : sets_1
Home
Index