Nuprl Lemma : hdf-sqequal8
∀[mk-hdf,a,s,X:Top].
(let b ⟵ a
in case null(b) of inl(x1) => let s' ⟵ s in <mk-hdf <X, s'>, s'> | inr(y1) => <mk-hdf <X, b>, b> ~ let b ⟵ a
in let s' ⟵ case null(b)
of inl(x1) =>
s
| inr(y1) =>
b
in <mk-hdf <X, s'>, s'>)
Proof
Definitions occuring in Statement :
null: null(as),
callbyvalueall: callbyvalueall,
uall: ∀[x:A]. B[x],
top: Top,
apply: f a,
pair: <a, b>,
decide: case b of inl(x) => s[x] | inr(y) => t[y],
sqequal: s ~ t
Definitions unfolded in proof :
null: null(as),
uall: ∀[x:A]. B[x],
so_lambda: so_lambda(x,y,z,w.t[x; y; z; w]),
member: t ∈ T,
so_apply: x[s1;s2;s3;s4],
so_lambda: λ2x.t[x],
top: Top,
so_apply: x[s],
uimplies: b supposing a,
strict4: strict4(F),
and: P ∧ Q,
all: ∀x:A. B[x],
implies: P ⇒ Q,
has-value: (a)↓,
prop: ℙ,
guard: {T},
or: P ∨ Q,
squash: ↓T,
bfalse: ff,
btrue: tt,
callbyvalueall: callbyvalueall,
evalall: evalall(t),
has-valueall: has-valueall(a)
Latex:
\mforall{}[mk-hdf,a,s,X:Top].
(let b \mleftarrow{}{} a
in case null(b) of inl(x1) => let s' \mleftarrow{}{} s in <mk-hdf <X, s'>, s'> | inr(y1) => <mk-hdf <X, b>, b>\000C \msim{} let b \mleftarrow{}{} a
in let s' \mleftarrow{}{} case null(b)
of inl(x1) =>
s
| inr(y1) =>
b
in <mk-hdf <X, s'>, s'>\000C)
Date html generated:
2016_05_16-AM-10_45_05
Last ObjectModification:
2016_01_17-AM-11_12_03
Theory : halting!dataflow
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