Nuprl Lemma : ses-flow-induction
∀s:SES. ∀es:EO+(Info).
∀[P:E ─→ E ─→ Atom1 ─→ ℙ]
((∀e1,e2:E.
((∀x,y:E.
(e1 c≤ x ⇒ x c≤ y ⇒ y c≤ e2 ⇒ ((e1 < x) ∨ (y < e2)) ⇒ (∀a:Atom1. (ses-flow(s;es;a;x;y) ⇒ P[x;y;a]))))
⇒ (∀a:Atom1. (ses-flow(s;es;a;e1;e2) ⇒ P[e1;e2;a]))))
⇒ {∀e1,e2:E. ∀a:Atom1. (ses-flow(s;es;a;e1;e2) ⇒ P[e1;e2;a])})
Proof
Definitions occuring in Statement :
ses-flow: ses-flow(s;es;a;e1;e2),
ses-info: Info,
security-event-structure: SES,
event-ordering+: EO+(Info),
es-causle: e c≤ e',
es-causl: (e < e'),
es-E: E,
atom: Atom$n,
uall: ∀[x:A]. B[x],
prop: ℙ,
guard: {T},
so_apply: x[s1;s2;s3],
all: ∀x:A. B[x],
implies: P ⇒ Q,
or: P ∨ Q,
function: x:A ─→ B[x]
Lemmas :
all_wf,
es-E_wf,
event-ordering+_subtype,
ses-info_wf,
es-causle_wf,
or_wf,
es-causl_wf,
ses-flow_wf,
event-ordering+_wf,
security-event-structure_wf,
less_than_transitivity1,
less_than_irreflexivity,
int_seg_wf,
decidable__equal_int,
subtype_rel-int_seg,
false_wf,
le_weakening,
subtract_wf,
int_seg_properties,
le_wf,
es-rank_wf,
nat_wf,
decidable__lt,
not-equal-2,
condition-implies-le,
minus-add,
minus-minus,
minus-one-mul,
add-swap,
add-commutes,
add-associates,
add_functionality_wrt_le,
zero-add,
le-add-cancel-alt,
less-iff-le,
le-add-cancel,
lelt_wf,
set_wf,
less_than_wf,
primrec-wf2,
decidable__le,
not-le-2,
sq_stable__le,
add-zero,
add-mul-special,
zero-mul,
es-rank_le,
zero-le-nat,
es-rank_property,
es-causle_weakening_locl,
es-causl_transitivity1,
es-causl_transitivity2,
es-causle_weakening,
es-causl_weakening
Latex:
\mforall{}s:SES. \mforall{}es:EO+(Info).
\mforall{}[P:E {}\mrightarrow{} E {}\mrightarrow{} Atom1 {}\mrightarrow{} \mBbbP{}]
((\mforall{}e1,e2:E.
((\mforall{}x,y:E.
(e1 c\mleq{} x
{}\mRightarrow{} x c\mleq{} y
{}\mRightarrow{} y c\mleq{} e2
{}\mRightarrow{} ((e1 < x) \mvee{} (y < e2))
{}\mRightarrow{} (\mforall{}a:Atom1. (ses-flow(s;es;a;x;y) {}\mRightarrow{} P[x;y;a]))))
{}\mRightarrow{} (\mforall{}a:Atom1. (ses-flow(s;es;a;e1;e2) {}\mRightarrow{} P[e1;e2;a]))))
{}\mRightarrow{} \{\mforall{}e1,e2:E. \mforall{}a:Atom1. (ses-flow(s;es;a;e1;e2) {}\mRightarrow{} P[e1;e2;a])\})
Date html generated:
2015_07_23-PM-00_05_08
Last ObjectModification:
2015_01_29-AM-07_50_38
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