Nuprl Lemma : pi_prefix_ind_wf
∀[A:Type]. ∀[R:A ─→ pi_prefix() ─→ ℙ]. ∀[v:pi_prefix()]. ∀[send:chan:Name ─→ var:Name ─→ {x:A| R[x;pisend(chan;var)]} ].
∀[rcv:chan:Name ─→ var:Name ─→ {x:A| R[x;pircv(chan;var)]} ].
(pi_prefix_ind(v;
pisend(chan,var)⇒ send[chan;var];
pircv(chan,var)⇒ rcv[chan;var]) ∈ {x:A| R[x;v]} )
Proof
Definitions occuring in Statement :
pi_prefix_ind: pi_prefix_ind,
pircv: pircv(chan;var),
pisend: pisend(chan;var),
pi_prefix: pi_prefix(),
name: Name,
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s1;s2],
member: t ∈ T,
set: {x:A| B[x]} ,
function: x:A ─→ B[x],
universe: Type
Definitions :
pi_prefix-definition,
pi_prefix-induction,
pi_prefix-ext,
ext-eq_weakening
Lemmas :
top_wf,
has-value_wf_base,
lifting-strict-atom_eq,
base_wf,
name_wf,
pisend_wf,
pircv_wf,
pi_prefix_wf,
all_wf,
set_wf,
subtype_rel-equal
Latex:
\mforall{}[A:Type]. \mforall{}[R:A {}\mrightarrow{} pi\_prefix() {}\mrightarrow{} \mBbbP{}]. \mforall{}[v:pi\_prefix()]. \mforall{}[send:chan:Name
{}\mrightarrow{} var:Name
{}\mrightarrow{} \{x:A| R[x;pisend(chan;var)]\} ].
\mforall{}[rcv:chan:Name {}\mrightarrow{} var:Name {}\mrightarrow{} \{x:A| R[x;pircv(chan;var)]\} ].
(pi\_prefix\_ind(v;
pisend(chan,var){}\mRightarrow{} send[chan;var];
pircv(chan,var){}\mRightarrow{} rcv[chan;var]) \mmember{} \{x:A| R[x;v]\} )
Date html generated:
2015_07_23-AM-11_31_47
Last ObjectModification:
2015_01_29-AM-00_53_21
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