Nuprl Lemma : set_leq_weakening_eq
∀[s:QOSet]. ∀[a,b:|s|]. a ≤ b supposing a = b ∈ |s|
Proof
Definitions occuring in Statement :
qoset: QOSet,
set_leq: a ≤ b,
set_car: |p|,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
set_leq: a ≤ b,
infix_ap: x f y,
qoset: QOSet,
dset: DSet,
implies: P ⇒ Q,
prop: ℙ
Lemmas referenced :
assert_witness,
set_le_wf,
equal_wf,
set_car_wf,
qoset_wf,
qoset_refl,
set_leq_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
sqequalHypSubstitution,
extract_by_obid,
isectElimination,
thin,
applyEquality,
setElimination,
rename,
hypothesisEquality,
hypothesis,
independent_functionElimination,
isect_memberEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
hyp_replacement,
Error :applyLambdaEquality
Latex:
\mforall{}[s:QOSet]. \mforall{}[a,b:|s|]. a \mleq{} b supposing a = b
Date html generated:
2016_10_21-AM-11_25_14
Last ObjectModification:
2016_07_12-PM-01_05_45
Theory : sets_1
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