Nuprl Lemma : set_leq_trans
∀[s:QOSet]. UniformlyTrans(|s|;x,y.x ≤ y)
Proof
Definitions occuring in Statement :
qoset: QOSet,
set_leq: a ≤ b,
set_car: |p|,
utrans: UniformlyTrans(T;x,y.E[x; y]),
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
utrans: UniformlyTrans(T;x,y.E[x; y]),
uall: ∀[x:A]. B[x],
member: t ∈ T,
implies: P ⇒ Q,
prop: ℙ,
qoset: QOSet,
dset: DSet,
set_leq: a ≤ b,
infix_ap: x f y,
uimplies: b supposing a
Lemmas referenced :
set_leq_wf,
assert_witness,
set_le_wf,
set_car_wf,
qoset_wf,
qoset_trans
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
setElimination,
rename,
hypothesisEquality,
hypothesis,
lambdaEquality,
dependent_functionElimination,
applyEquality,
independent_functionElimination,
isect_memberEquality,
because_Cache,
independent_isectElimination
Latex:
\mforall{}[s:QOSet]. UniformlyTrans(|s|;x,y.x \mleq{} y)
Date html generated:
2016_05_15-PM-00_04_42
Last ObjectModification:
2015_12_26-PM-11_28_06
Theory : sets_1
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