### Nuprl Lemma : hdf-sqequal2-weak

`∀[F,G,H:Base].`
`  (fix((λmk-hdf,s0. case s0 of inl(y) => inl (λa.let X',bs = y a in let out ⟵ G[bs] in <mk-hdf X', out>) | inr(z) => H[\000Cz])) `
`   fix((λmk-hdf.(inl (λm.<mk-hdf, F[m]>)))) ~ fix((λmk-hdf.(inl (λa.let out ⟵ G[F[a]]`
`                                                                    in <mk-hdf, out>)))))`

Proof

Definitions occuring in Statement :  callbyvalueall: callbyvalueall uall: `∀[x:A]. B[x]` so_apply: `x[s]` apply: `f a` fix: `fix(F)` lambda: `λx.A[x]` spread: spread def pair: `<a, b>` decide: `case b of inl(x) => s[x] | inr(y) => t[y]` inl: `inl x` base: `Base` sqequal: `s ~ t`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` so_lambda: `λ2x.t[x]` top: `Top` so_apply: `x[s]`

Latex:
\mforall{}[F,G,H:Base].
(fix((\mlambda{}mk-hdf,s0.  case  s0
of  inl(y)  =>
inl  (\mlambda{}a.let  X',bs  =  y  a
in  let  out  \mleftarrow{}{}  G[bs]
in  <mk-hdf  X',  out>)
|  inr(z)  =>
H[z]))
fix((\mlambda{}mk-hdf.(inl  (\mlambda{}m.<mk-hdf,  F[m]>))))  \msim{}  fix((\mlambda{}mk-hdf.(inl  (\mlambda{}a.let  out  \mleftarrow{}{}  G[F[a]]
in  <mk-hdf,  out>)))))

Date html generated: 2016_05_16-AM-10_50_46
Last ObjectModification: 2015_12_28-PM-07_38_15

Theory : halting!dataflow

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