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 unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
pi_prefix_ind: pi_prefix_ind,
so_apply: x[s1;s2],
pi_prefix-definition,
pi_prefix-induction,
pi_prefix-ext,
ext-eq_weakening,
eq_atom: x =a y,
bool_cases_sqequal,
eqff_to_assert,
any: any x,
btrue: tt,
bfalse: ff,
it: ⋅,
top: Top,
all: ∀x:A. B[x],
implies: P ⇒ Q,
has-value: (a)↓,
so_lambda: so_lambda(x,y,z,w.t[x; y; z; w]),
so_apply: x[s1;s2;s3;s4],
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a,
strict4: strict4(F),
and: P ∧ Q,
prop: ℙ,
guard: {T},
or: P ∨ Q,
squash: ↓T,
subtype_rel: A ⊆r B
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:
2016_05_17-AM-11_20_23
Last ObjectModification:
2016_01_18-AM-07_49_11
Theory : event-logic-applications
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