Nuprl Lemma : id-member-normal-form
∀[x,L:Top]. (rec-case(L) of [] => ff | a::_ => r.if a=2 x then tt else r ~ x ∈b L)
Proof
Definitions occuring in Statement :
id-deq: IdDeq,
deq-member: x ∈b L,
list_ind: list_ind,
atom_eq: atomeqn def,
bfalse: ff,
btrue: tt,
uall: ∀[x:A]. B[x],
top: Top,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
list_ind: list_ind,
btrue: tt,
it: ⋅,
bfalse: ff,
deq-member: x ∈b L,
reduce: reduce(f;k;as),
bor: p ∨bq,
ifthenelse: if b then t else f fi ,
id-deq: IdDeq,
atom2-deq: Atom2Deq,
eq_atom: eq_atom$n(x;y),
so_lambda: so_lambda(x,y,z,w.t[x; y; z; w]),
so_apply: x[s1;s2;s3;s4],
so_lambda: λ2x.t[x],
top: Top,
so_apply: x[s],
uimplies: b supposing a,
strict4: strict4(F),
and: P ∧ Q,
all: ∀x:A. B[x],
implies: P ⇒ Q,
has-value: (a)↓,
prop: ℙ,
guard: {T},
or: P ∨ Q,
squash: ↓T
Latex:
\mforall{}[x,L:Top]. (rec-case(L) of [] => ff | a::$_{}$ => r.if a=2 x then tt else r \msim{} \000Cx \mmember{}\msubb{} L)
Date html generated:
2016_05_16-AM-11_02_07
Last ObjectModification:
2016_01_17-PM-03_47_31
Theory : event-ordering
Home
Index