Nuprl Lemma : pi-trans_wf
∀[l_loc:Id]. ∀[P:pi_term()]. (pi-trans(l_loc;P) ∈ Id ⟶ Name ⟶ (Name List) ⟶ pi-process())
Proof
Definitions occuring in Statement :
pi-trans: pi-trans(l_loc;P),
pi-process: pi-process(),
pi_term: pi_term(),
Id: Id,
name: Name,
list: T List,
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ⟶ B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
nat: ℕ,
implies: P ⇒ Q,
false: False,
ge: i ≥ j ,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
not: ¬A,
top: Top,
and: P ∧ Q,
prop: ℙ,
subtype_rel: A ⊆r B,
guard: {T},
decidable: Dec(P),
or: P ∨ Q,
ext-eq: A ≡ B,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
sq_type: SQType(T),
eq_atom: x =a y,
ifthenelse: if b then t else f fi ,
pizero: pizero(),
pi-rank: pi-rank(p),
pi_term_ind: pi_term_ind(v;zero;pre,body,rec1....;left,right,rec2,rec3....;left,right,rec4,rec5....;body,rec6....;name,body,rec7....),
pi-trans: pi-trans(l_loc;P),
pizero?: pizero?(v),
pi1: fst(t),
pipar?: pipar?(v),
pipar-left: pipar-left(v),
pi2: snd(t),
pipar-right: pipar-right(v),
pirep?: pirep?(v),
pirep-body: pirep-body(v),
pinew?: pinew?(v),
pinew-name: pinew-name(v),
pinew-body: pinew-body(v),
pioption?: pioption?(v),
picomm?: picomm?(v),
bfalse: ff,
bnot: ¬bb,
assert: ↑b,
picomm: picomm(pre;body),
so_lambda: λ2x.t[x],
so_apply: x[s],
pioption: pioption(left;right),
pipar: pipar(left;right),
let: let,
less_than: a < b,
squash: ↓T,
pirep: pirep(body),
pinew: pinew(name;body),
iff: P ⇐⇒ Q,
le: A ≤ B,
less_than': less_than'(a;b)
Latex:
\mforall{}[l$_{loc}$:Id]. \mforall{}[P:pi\_term()]. (pi-trans(l$_{loc}$;P) \mmember{} I\000Cd {}\mrightarrow{} Name {}\mrightarrow{} (Name List) {}\mrightarrow{} pi-process())
Date html generated:
2016_05_17-AM-11_35_14
Last ObjectModification:
2016_01_18-AM-07_48_05
Theory : event-logic-applications
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