Nuprl Lemma : es-increasing-sequence2
∀es:EO. ∀m:ℕ+. ∀f:ℕm ⟶ E. ((∀i:ℕm - 1. (f i <loc f (i + 1))) ⇒ (∀i:ℕm. ∀j:ℕi + 1. f j ≤loc f i ))
Proof
Definitions occuring in Statement :
es-le: e ≤loc e' ,
es-locl: (e <loc e'),
es-E: E,
event_ordering: EO,
int_seg: {i..j-},
nat_plus: ℕ+,
all: ∀x:A. B[x],
implies: P ⇒ Q,
apply: f a,
function: x:A ⟶ B[x],
subtract: n - m,
add: n + m,
natural_number: $n
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
int_seg: {i..j-},
decidable: Dec(P),
or: P ∨ Q,
uall: ∀[x:A]. B[x],
nat_plus: ℕ+,
prop: ℙ,
so_lambda: λ2x.t[x],
lelt: i ≤ j < k,
and: P ∧ Q,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A,
top: Top,
uiff: uiff(P;Q),
subtract: n - m,
so_apply: x[s],
sq_type: SQType(T),
guard: {T},
le: A ≤ B,
less_than: a < b,
es-le: e ≤loc e' ,
es-locl: (e <loc e')
Latex:
\mforall{}es:EO. \mforall{}m:\mBbbN{}\msupplus{}. \mforall{}f:\mBbbN{}m {}\mrightarrow{} E.
((\mforall{}i:\mBbbN{}m - 1. (f i <loc f (i + 1))) {}\mRightarrow{} (\mforall{}i:\mBbbN{}m. \mforall{}j:\mBbbN{}i + 1. f j \mleq{}loc f i ))
Date html generated:
2016_05_16-AM-09_55_02
Last ObjectModification:
2016_01_17-PM-01_22_49
Theory : new!event-ordering
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