### Nuprl Lemma : comb_for_set_blt_wf

`λp,a,b,z. (a <b b) ∈ p:PosetSig ⟶ a:|p| ⟶ b:|p| ⟶ (↓True) ⟶ 𝔹`

Proof

Definitions occuring in Statement :  set_blt: `a <b b` set_car: `|p|` poset_sig: `PosetSig` bool: `𝔹` squash: `↓T` true: `True` member: `t ∈ T` lambda: `λx.A[x]` function: `x:A ⟶ B[x]`
Definitions unfolded in proof :  member: `t ∈ T` squash: `↓T` uall: `∀[x:A]. B[x]` prop: `ℙ`
Lemmas referenced :  set_blt_wf squash_wf true_wf set_car_wf poset_sig_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity lambdaEquality sqequalHypSubstitution imageElimination cut lemma_by_obid isectElimination thin hypothesisEquality equalityTransitivity hypothesis equalitySymmetry

Latex:
\mlambda{}p,a,b,z.  (a  <\msubb{}  b)  \mmember{}  p:PosetSig  {}\mrightarrow{}  a:|p|  {}\mrightarrow{}  b:|p|  {}\mrightarrow{}  (\mdownarrow{}True)  {}\mrightarrow{}  \mBbbB{}

Date html generated: 2016_05_15-PM-00_04_17
Last ObjectModification: 2015_12_26-PM-11_28_40

Theory : sets_1

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