Nuprl Lemma : hdf-sqequal1
∀[F:Top]. (hdf-base(m.F[m]) ~ fix((λmk-hdf.(inl (λm.<mk-hdf, F[m]>)))))
Proof
Definitions occuring in Statement :
hdf-base: hdf-base(m.F[m]),
uall: ∀[x:A]. B[x],
top: Top,
so_apply: x[s],
fix: fix(F),
lambda: λx.A[x],
pair: <a, b>,
inl: inl x,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
hdf-base: hdf-base(m.F[m]),
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),
so_apply: x[s],
it: ⋅,
all: ∀x:A. B[x],
guard: {T},
int_seg: {i..j-},
lelt: i ≤ j < k,
and: P ∧ Q,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
implies: P ⇒ Q,
not: ¬A,
top: Top,
prop: ℙ,
decidable: Dec(P),
or: P ∨ Q,
subtype_rel: A ⊆r B,
le: A ≤ B,
less_than': less_than'(a;b),
nat: ℕ,
ge: i ≥ j ,
sq_type: SQType(T),
so_lambda: λ2x.t[x]
Latex:
\mforall{}[F:Top]. (hdf-base(m.F[m]) \msim{} fix((\mlambda{}mk-hdf.(inl (\mlambda{}m.<mk-hdf, F[m]>)))))
Date html generated:
2016_05_16-AM-10_44_55
Last ObjectModification:
2016_01_17-AM-11_12_23
Theory : halting!dataflow
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