Nuprl Lemma : pi-subst-aux_wf
∀[p:pi_term()]. (pi-subst-aux(p) ∈ (Name List) ⟶ ((Name × Name) List) ⟶ pi_term())
Proof
Definitions occuring in Statement :
pi-subst-aux: pi-subst-aux(p),
pi_term: pi_term(),
name: Name,
list: T List,
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ⟶ B[x],
product: x:A × B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
pi-subst-aux: pi-subst-aux(p),
let: let,
so_lambda: so_lambda(x,y,z.t[x; y; z]),
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
ifthenelse: if b then t else f fi ,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
iff: P ⇐⇒ Q,
subtype_rel: A ⊆r B,
prop: ℙ,
pi1: fst(t),
bfalse: ff,
exists: ∃x:A. B[x],
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
false: False,
not: ¬A,
rev_implies: P ⇐ Q,
so_apply: x[s1;s2;s3],
so_lambda: so_lambda(x,y,z,w.t[x; y; z; w]),
so_apply: x[s1;s2;s3;s4]
Latex:
\mforall{}[p:pi\_term()]. (pi-subst-aux(p) \mmember{} (Name List) {}\mrightarrow{} ((Name \mtimes{} Name) List) {}\mrightarrow{} pi\_term())
Date html generated:
2016_05_17-AM-11_25_00
Last ObjectModification:
2015_12_29-PM-06_53_51
Theory : event-logic-applications
Home
Index