Nuprl Lemma : set_leq_wf
∀[p:PosetSig]. ∀[a,b:|p|]. (a ≤ b ∈ ℙ)
Proof
Definitions occuring in Statement :
set_leq: a ≤ b,
set_car: |p|,
poset_sig: PosetSig,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T
Definitions unfolded in proof :
set_leq: a ≤ b,
uall: ∀[x:A]. B[x],
member: t ∈ T,
infix_ap: x f y
Lemmas referenced :
assert_wf,
set_le_wf,
set_car_wf,
poset_sig_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
applyEquality,
hypothesisEquality,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[p:PosetSig]. \mforall{}[a,b:|p|]. (a \mleq{} b \mmember{} \mBbbP{})
Date html generated:
2016_05_15-PM-00_04_10
Last ObjectModification:
2015_12_26-PM-11_28_45
Theory : sets_1
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