Nuprl Lemma : pred-hd-es-open-interval
∀[es:EO]. ∀[e1,e2:E]. pred(hd((e1, e2))) = e1 ∈ E supposing ||(e1, e2)|| > 0
Proof
Definitions occuring in Statement :
es-open-interval: (e, e'),
es-pred: pred(e),
es-E: E,
event_ordering: EO,
hd: hd(l),
length: ||as||,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
gt: i > j,
natural_number: $n,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
all: ∀x:A. B[x],
gt: i > j,
ge: i ≥ j ,
decidable: Dec(P),
or: P ∨ Q,
less_than: a < b,
squash: ↓T,
and: P ∧ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
implies: P ⇒ Q,
not: ¬A,
top: Top,
prop: ℙ,
iff: P ⇐⇒ Q,
assert: ↑b,
ifthenelse: if b then t else f fi ,
btrue: tt,
less_than': less_than'(a;b),
cons: [a / b],
bfalse: ff,
guard: {T},
es-locl: (e <loc e'),
es-open-interval: (e, e'),
rev_implies: P ⇐ Q,
cand: A c∧ B,
sq_type: SQType(T),
l_member: (x ∈ l),
nat: ℕ,
le: A ≤ B,
l-ordered: l-ordered(T;x,y.R[x; y];L),
l_before: x before y ∈ l,
sublist: L1 ⊆ L2,
int_seg: {i..j-},
bool: 𝔹,
unit: Unit,
it: ⋅,
uiff: uiff(P;Q),
nequal: a ≠ b ∈ T ,
int_upper: {i...},
lelt: i ≤ j < k,
bnot: ¬bb,
increasing: increasing(f;k),
subtract: n - m,
select: L[n],
eq_int: (i =z j),
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s]
Latex:
\mforall{}[es:EO]. \mforall{}[e1,e2:E]. pred(hd((e1, e2))) = e1 supposing ||(e1, e2)|| > 0
Date html generated:
2016_05_16-AM-09_36_31
Last ObjectModification:
2016_01_17-PM-01_29_14
Theory : new!event-ordering
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