Nuprl Lemma : es-pred-less-base
∀es:EO. ∀e:es-base-E(es). ((¬(pred(e) = e ∈ es-base-E(es))) ⇒ (pred(e) < e))
Proof
Definitions occuring in Statement :
es-pred: pred(e),
es-causl: (e < e'),
es-base-E: es-base-E(es),
event_ordering: EO,
all: ∀x:A. B[x],
not: ¬A,
implies: P ⇒ Q,
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
member: t ∈ T,
strongwellfounded: SWellFounded(R[x; y]),
exists: ∃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),
not: ¬A,
top: Top,
and: P ∧ Q,
prop: ℙ,
guard: {T},
es-causl: (e < e'),
squash: ↓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,
es-pred: pred(e),
let: let,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
bfalse: ff,
sq_type: SQType(T),
bnot: ¬bb,
assert: ↑b,
es-eq-E: e = e',
deq: EqDecider(T)
Latex:
\mforall{}es:EO. \mforall{}e:es-base-E(es). ((\mneg{}(pred(e) = e)) {}\mRightarrow{} (pred(e) < e))
Date html generated:
2016_05_16-AM-09_16_25
Last ObjectModification:
2016_01_17-PM-01_31_54
Theory : new!event-ordering
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