Nuprl Lemma : hdf-base-transformation2
∀[F:Top]. (hdf-base(m.F[m]) ~ fix((λmk-hdf,s. (inl (λa.cbva_seq(λx.⊥; λg.<mk-hdf Ax, F[a]>; 0))))) Ax)
Proof
Definitions occuring in Statement :
hdf-base: hdf-base(m.F[m]),
bottom: ⊥,
uall: ∀[x:A]. B[x],
top: Top,
so_apply: x[s],
apply: f a,
fix: fix(F),
lambda: λx.A[x],
pair: <a, b>,
inl: inl x,
natural_number: $n,
sqequal: s ~ t,
axiom: Ax,
cbva_seq: cbva_seq(L; F; m)
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
cbva_seq: cbva_seq(L; F; m),
hdf-base: hdf-base(m.F[m]),
it: ⋅,
mk-hdf: mk-hdf(s,m.G[s; m];st.H[st];s0),
ifthenelse: if b then t else f fi ,
bfalse: ff,
hdf-run: hdf-run(P),
callbyvalueall_seq: callbyvalueall_seq(L;G;F;n;m),
le_int: i ≤z j,
lt_int: i <z j,
bnot: ¬bb,
btrue: tt,
nat: ℕ,
implies: P ⇒ Q,
false: False,
ge: i ≥ j ,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
not: ¬A,
all: ∀x:A. B[x],
top: Top,
and: P ∧ Q,
prop: ℙ,
decidable: Dec(P),
or: P ∨ Q,
nat_plus: ℕ+,
so_apply: x[s]
Latex:
\mforall{}[F:Top]. (hdf-base(m.F[m]) \msim{} fix((\mlambda{}mk-hdf,s. (inl (\mlambda{}a.cbva\_seq(\mlambda{}x.\mbot{}; \mlambda{}g.<mk-hdf Ax, F[a]> 0))))) A\000Cx)
Date html generated:
2016_05_16-AM-10_45_23
Last ObjectModification:
2016_01_17-AM-11_12_00
Theory : halting!dataflow
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