### Nuprl Lemma : assert_of_set_leq

`∀[p:PosetSig]. ∀[a,b:|p|].  uiff(↑(a (≤b) b);a ≤ b)`

Proof

Definitions occuring in Statement :  set_leq: `a ≤ b` set_le: `≤b` set_car: `|p|` poset_sig: `PosetSig` assert: `↑b` uiff: `uiff(P;Q)` uall: `∀[x:A]. B[x]` infix_ap: `x f y`
Definitions unfolded in proof :  set_leq: `a ≤ b` uall: `∀[x:A]. B[x]` member: `t ∈ T` uiff: `uiff(P;Q)` and: `P ∧ Q` uimplies: `b supposing a` infix_ap: `x f y` implies: `P `` Q` prop: `ℙ`
Lemmas referenced :  assert_witness set_le_wf assert_wf set_car_wf poset_sig_wf
Rules used in proof :  sqequalSubstitution sqequalRule sqequalReflexivity sqequalTransitivity computationStep isect_memberFormation introduction cut independent_pairFormation hypothesis lemma_by_obid sqequalHypSubstitution isectElimination thin applyEquality hypothesisEquality independent_functionElimination because_Cache productElimination independent_pairEquality isect_memberEquality equalityTransitivity equalitySymmetry

Latex:
\mforall{}[p:PosetSig].  \mforall{}[a,b:|p|].    uiff(\muparrow{}(a  (\mleq{}\msubb{})  b);a  \mleq{}  b)

Date html generated: 2016_05_15-PM-00_04_13
Last ObjectModification: 2015_12_26-PM-11_28_44

Theory : sets_1

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