### Nuprl Lemma : set_leq_antisymmetry

`∀[s:POSet{i}]. ∀[a,b:|s|].  (a = b ∈ |s|) supposing ((b ≤ a) and (a ≤ b))`

Proof

Definitions occuring in Statement :  poset: `POSet{i}` 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` uanti_sym: `UniformlyAntiSym(T;x,y.R[x; y])` uimplies: `b supposing a` prop: `ℙ` poset: `POSet{i}` qoset: `QOSet` dset: `DSet`
Lemmas referenced :  poset_properties set_leq_wf set_car_wf poset_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut lemma_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality hypothesis sqequalRule isect_memberEquality axiomEquality setElimination rename equalityTransitivity equalitySymmetry

Latex:
\mforall{}[s:POSet\{i\}].  \mforall{}[a,b:|s|].    (a  =  b)  supposing  ((b  \mleq{}  a)  and  (a  \mleq{}  b))

Date html generated: 2016_05_15-PM-00_05_07
Last ObjectModification: 2015_12_26-PM-11_27_53

Theory : sets_1

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