Nuprl Lemma : iseg-es-interval
∀[es:EO]. ∀[L:E List]. ∀[e1,e2:E]. (L = [e1, last(L)] ∈ (E List)) supposing ((¬↑null(L)) and L ≤ [e1, e2])
Proof
Definitions occuring in Statement :
es-interval: [e, e'],
es-E: E,
event_ordering: EO,
iseg: l1 ≤ l2,
last: last(L),
null: null(as),
list: T List,
assert: ↑b,
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,
uimplies: b supposing a,
es-interval: [e, e'],
all: ∀x:A. B[x],
implies: P ⇒ Q,
es-le-before: ≤loc(e),
exists: ∃x:A. B[x],
and: P ∧ Q,
prop: ℙ,
subtype_rel: A ⊆r B,
top: Top,
true: True,
so_lambda: λ2x.t[x],
so_apply: x[s],
squash: ↓T,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
not: ¬A,
uiff: uiff(P;Q),
l_member: (x ∈ l),
cand: A c∧ B,
nat: ℕ,
decidable: Dec(P),
or: P ∨ Q,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
int_seg: {i..j-},
lelt: i ≤ j < k,
ge: i ≥ j ,
less_than: a < b,
satisfiable_int_formula: satisfiable_int_formula(fmla),
false: False,
le: A ≤ B,
es-locl: (e <loc e'),
last: last(L),
cons: [a / b],
subtract: n - m,
less_than': less_than'(a;b)
Latex:
\mforall{}[es:EO]. \mforall{}[L:E List]. \mforall{}[e1,e2:E]. (L = [e1, last(L)]) supposing ((\mneg{}\muparrow{}null(L)) and L \mleq{} [e1, e2])
Date html generated:
2016_05_16-AM-09_38_34
Last ObjectModification:
2016_01_17-PM-01_28_26
Theory : new!event-ordering
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