Nuprl Lemma : assert-es-first
∀[es:EO]. ∀[e:E]. uiff(↑first(e);∀[e':E]. ¬(e' < e) supposing loc(e') = loc(e) ∈ Id)
Proof
Definitions occuring in Statement :
es-first: first(e),
es-causl: (e < e'),
es-loc: loc(e),
es-E: E,
event_ordering: EO,
Id: Id,
assert: ↑b,
uiff: uiff(P;Q),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
not: ¬A,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
not: ¬A,
implies: P ⇒ Q,
false: False,
prop: ℙ,
es-E: E,
es-base-E: es-base-E(es),
so_lambda: λ2x.t[x],
so_apply: x[s],
es-first: first(e),
all: ∀x:A. B[x],
strongwellfounded: SWellFounded(R[x; y]),
exists: ∃x:A. B[x],
nat: ℕ,
ge: i ≥ j ,
satisfiable_int_formula: satisfiable_int_formula(fmla),
top: Top,
guard: {T},
subtype_rel: A ⊆r B,
int_seg: {i..j-},
lelt: i ≤ j < k,
le: A ≤ B,
less_than': less_than'(a;b),
decidable: Dec(P),
or: P ∨ Q,
less_than: a < b,
squash: ↓T,
es-pred: pred(e),
let: let,
es-eq-E: e = e',
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
ifthenelse: if b then t else f fi ,
bfalse: ff,
sq_type: SQType(T),
bnot: ¬bb,
assert: ↑b,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
rev_uimplies: rev_uimplies(P;Q),
es-dom: es-dom(es),
sq_stable: SqStable(P)
Latex:
\mforall{}[es:EO]. \mforall{}[e:E]. uiff(\muparrow{}first(e);\mforall{}[e':E]. \mneg{}(e' < e) supposing loc(e') = loc(e))
Date html generated:
2016_05_16-AM-09_17_12
Last ObjectModification:
2016_01_17-PM-01_33_01
Theory : new!event-ordering
Home
Index