Nuprl Lemma : pi_prefix-definition
∀[A:Type]. ∀[R:A ─→ pi_prefix() ─→ ℙ].
((∀chan,var:Name. {x:A| R[x;pisend(chan;var)]} )
⇒ (∀chan,var:Name. {x:A| R[x;pircv(chan;var)]} )
⇒ {∀v:pi_prefix(). {x:A| R[x;v]} })
Proof
Definitions occuring in Statement :
pircv: pircv(chan;var),
pisend: pisend(chan;var),
pi_prefix: pi_prefix(),
name: Name,
uall: ∀[x:A]. B[x],
prop: ℙ,
guard: {T},
so_apply: x[s1;s2],
all: ∀x:A. B[x],
implies: P ⇒ Q,
set: {x:A| B[x]} ,
function: x:A ─→ B[x],
universe: Type
Lemmas :
pi_prefix-induction,
set_wf,
pi_prefix_wf,
all_wf,
name_wf,
pircv_wf,
pisend_wf
Latex:
\mforall{}[A:Type]. \mforall{}[R:A {}\mrightarrow{} pi\_prefix() {}\mrightarrow{} \mBbbP{}].
((\mforall{}chan,var:Name. \{x:A| R[x;pisend(chan;var)]\} )
{}\mRightarrow{} (\mforall{}chan,var:Name. \{x:A| R[x;pircv(chan;var)]\} )
{}\mRightarrow{} \{\mforall{}v:pi\_prefix(). \{x:A| R[x;v]\} \})
Date html generated:
2015_07_23-AM-11_31_45
Last ObjectModification:
2015_01_29-AM-00_53_16
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