Nuprl Lemma : hd-es-le-before
∀es:EO. ∀e,fst:E. ((↑first(fst)) ⇒ fst ≤loc e ⇒ (hd(≤loc(e)) = fst ∈ E))
Proof
Definitions occuring in Statement :
es-le-before: ≤loc(e),
es-le: e ≤loc e' ,
es-first: first(e),
es-E: E,
event_ordering: EO,
hd: hd(l),
assert: ↑b,
all: ∀x:A. B[x],
implies: P ⇒ Q,
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
strongwellfounded: SWellFounded(R[x; y]),
exists: ∃x:A. B[x],
uall: ∀[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},
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-le-before: ≤loc(e),
es-before: before(e),
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
append: as @ bs,
so_lambda: so_lambda(x,y,z.t[x; y; z]),
so_apply: x[s1;s2;s3],
bfalse: ff,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
es-le: e ≤loc e' ,
so_lambda: λ2x.t[x],
so_apply: x[s],
cons: [a / b]
Latex:
\mforall{}es:EO. \mforall{}e,fst:E. ((\muparrow{}first(fst)) {}\mRightarrow{} fst \mleq{}loc e {}\mRightarrow{} (hd(\mleq{}loc(e)) = fst))
Date html generated:
2016_05_16-AM-09_35_06
Last ObjectModification:
2016_01_17-PM-01_28_48
Theory : new!event-ordering
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