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,
nat_plus: ℕ+,
int_seg: {i..j-},
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
Lemmas :
es-increasing-sequence,
decidable__equal_int,
int_seg_wf,
all_wf,
subtract_wf,
es-locl_wf,
decidable__lt,
false_wf,
less-iff-le,
condition-implies-le,
add-associates,
minus-add,
minus-one-mul,
add-swap,
add-commutes,
add_functionality_wrt_le,
le-add-cancel2,
lelt_wf,
decidable__le,
not-le-2,
sq_stable__le,
zero-add,
add-zero,
le-add-cancel,
nat_plus_wf,
subtype_base_sq,
int_subtype_base,
es-le-self,
less_than_transitivity2,
le_weakening,
equal_wf,
not-equal-2
\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:
2015_07_17-AM-08_53_29
Last ObjectModification:
2015_01_27-PM-01_18_41
Home
Index