Nuprl Lemma : qoset_refl
∀[s:QOSet]. ∀[a:|s|]. (a ≤ a)
Proof
Definitions occuring in Statement :
qoset: QOSet,
set_leq: a ≤ b,
set_car: |p|,
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]),
set_leq: a ≤ b,
infix_ap: x f y,
qoset: QOSet,
dset: DSet,
implies: P ⇒ Q
Lemmas referenced :
qoset_properties,
assert_witness,
set_le_wf,
set_car_wf,
qoset_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
productElimination,
sqequalRule,
isect_memberEquality,
applyEquality,
setElimination,
rename,
independent_functionElimination
Latex:
\mforall{}[s:QOSet]. \mforall{}[a:|s|]. (a \mleq{} a)
Date html generated:
2016_05_15-PM-00_04_34
Last ObjectModification:
2015_12_26-PM-11_28_12
Theory : sets_1
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