Nuprl Lemma : hd-es-interval
∀[es:EO]. ∀[e,e':E]. hd([e, e']) = e ∈ E supposing e ≤loc e'
Proof
Definitions occuring in Statement :
es-interval: [e, e'],
es-le: e ≤loc e' ,
es-E: E,
event_ordering: EO,
hd: hd(l),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
prop: ℙ,
and: P ∧ Q,
cand: A c∧ B,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
l_member: (x ∈ l),
exists: ∃x:A. B[x],
nat: ℕ,
decidable: Dec(P),
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
top: Top,
ge: i ≥ j ,
less_than: a < b,
squash: ↓T,
satisfiable_int_formula: satisfiable_int_formula(fmla),
false: False,
not: ¬A,
int_seg: {i..j-},
lelt: i ≤ j < k,
le: A ≤ B,
less_than': less_than'(a;b),
select: L[n],
nil: [],
it: ⋅,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
cons: [a / b]
Latex:
\mforall{}[es:EO]. \mforall{}[e,e':E]. hd([e, e']) = e supposing e \mleq{}loc e'
Date html generated:
2016_05_16-AM-09_32_20
Last ObjectModification:
2016_01_17-PM-01_29_57
Theory : new!event-ordering
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