Nuprl Lemma : es-increasing-sequence
∀es:EO. ∀m:ℕ+. ∀f:ℕm ─→ E. ((∀i:ℕm - 1. (f i <loc f (i + 1))) ⇒ (∀i:ℕm. ∀j:ℕi. (f j <loc f i)))
Proof
Definitions occuring in Statement :
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 :
all_wf,
int_seg_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,
es-E_wf,
nat_plus_wf,
event_ordering_wf,
nat_properties,
less_than_transitivity1,
less_than_irreflexivity,
ge_wf,
less_than_wf,
le_wf,
not-ge-2,
minus-minus,
nat_wf,
decidable__equal_int,
subtype_base_sq,
int_subtype_base,
es-locl_transitivity2,
es-le_weakening
\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. (f j <loc f i)))
Date html generated:
2015_07_17-AM-08_53_26
Last ObjectModification:
2015_01_27-PM-01_18_50
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