Nuprl Lemma : pi_prefix-induction

[P:pi_prefix() ⟶ ℙ]
  ((∀chan,var:Name.  P[pisend(chan;var)])  (∀chan,var:Name.  P[pircv(chan;var)])  {∀v:pi_prefix(). P[v]})


Proof




Definitions occuring in Statement :  pircv: pircv(chan;var) pisend: pisend(chan;var) pi_prefix: pi_prefix() name: Name uall: [x:A]. B[x] prop: guard: {T} so_apply: x[s] all: x:A. B[x] implies:  Q function: x:A ⟶ B[x]
Definitions unfolded in proof :  uall: [x:A]. B[x] implies:  Q guard: {T} all: x:A. B[x] ext-eq: A ≡ B and: P ∧ Q member: t ∈ T subtype_rel: A ⊆B bool: 𝔹 unit: Unit it: btrue: tt uiff: uiff(P;Q) uimplies: supposing a sq_type: SQType(T) eq_atom: =a y ifthenelse: if then else fi  pisend: pisend(chan;var) bfalse: ff exists: x:A. B[x] prop: or: P ∨ Q bnot: ¬bb assert: b false: False pircv: pircv(chan;var)

Latex:
\mforall{}[P:pi\_prefix()  {}\mrightarrow{}  \mBbbP{}]
    ((\mforall{}chan,var:Name.    P[pisend(chan;var)])
    {}\mRightarrow{}  (\mforall{}chan,var:Name.    P[pircv(chan;var)])
    {}\mRightarrow{}  \{\mforall{}v:pi\_prefix().  P[v]\})



Date html generated: 2016_05_17-AM-11_20_16
Last ObjectModification: 2015_12_29-PM-06_58_31

Theory : event-logic-applications


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