Nuprl Lemma : pi-bar-trans_wf
∀[l_loc:Id]. ∀[P,Q:pi_term()]. ∀[g:{R:pi_term()| pi-rank(R) < pi-rank(pipar(P;Q))}
⟶ Id
⟶ Name
⟶ (Name List)
⟶ pi-process()].
(pi-bar-trans(l_loc;P;Q;g) ∈ Id ⟶ Name ⟶ (Name List) ⟶ pi-process())
Proof
Definitions occuring in Statement :
pi-bar-trans: pi-bar-trans(l_loc;P;Q;g),
pi-process: pi-process(),
pi-rank: pi-rank(p),
pipar: pipar(left;right),
pi_term: pi_term(),
Id: Id,
name: Name,
list: T List,
less_than: a < b,
uall: ∀[x:A]. B[x],
member: t ∈ T,
set: {x:A| B[x]} ,
function: x:A ⟶ B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
pi-bar-trans: pi-bar-trans(l_loc;P;Q;g),
subtype_rel: A ⊆r B,
nat: ℕ,
prop: ℙ,
int_seg: {i..j-},
lelt: i ≤ j < k,
and: P ∧ Q,
le: A ≤ B,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
less_than: a < b,
squash: ↓T,
true: True,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
sq_type: SQType(T),
guard: {T},
eq_int: (i =z j),
band: p ∧b q,
ifthenelse: if b then t else f fi ,
btrue: tt,
bfalse: ff,
piM: piM(T),
bool: 𝔹,
unit: Unit,
it: ⋅,
uiff: uiff(P;Q),
so_lambda: λ2x.t[x],
so_apply: x[s],
type-monotone: Monotone(T.F[T]),
pi-process: pi-process(),
PiDataVal: PiDataVal(),
pMsg: pMsg(P.M[P]),
exists: ∃x:A. B[x],
bnot: ¬bb,
assert: ↑b,
let: let,
make-lg: make-lg(L),
lg-size: lg-size(g),
top: Top,
satisfiable_int_formula: satisfiable_int_formula(fmla),
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
ge: i ≥ j
Latex:
\mforall{}[l$_{loc}$:Id]. \mforall{}[P,Q:pi\_term()]. \mforall{}[g:\{R:pi\_term()| pi-rank(R) < pi-rank(pipar(\000CP;Q))\}
{}\mrightarrow{} Id
{}\mrightarrow{} Name
{}\mrightarrow{} (Name List)
{}\mrightarrow{} pi-process()].
(pi-bar-trans(l$_{loc}$;P;Q;g) \mmember{} Id {}\mrightarrow{} Name {}\mrightarrow{} (Name List) {}\mrightarrow{} pi-process())
Date html generated:
2016_05_17-AM-11_34_13
Last ObjectModification:
2016_01_18-AM-07_50_47
Theory : event-logic-applications
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