Nuprl Lemma : es-cut-induction
∀[Info:Type]
∀es:EO+(Info). ∀X:EClass(Top). ∀f:sys-antecedent(es;X).
∀[P:Cut(X;f) ─→ ℙ]
(((∃R:E(X) ─→ E(X) ─→ ℙ. (Linorder(E(X);x,y.R[x;y]) ∧ (∀x,y:E(X). Dec(R[x;y])))) ∨ (∀c:Cut(X;f). SqStable(P[c])))
⇒ P[{}]
⇒ (∀c:Cut(X;f). ∀e:E(X). (P[c] ⇒ P[c+e] supposing add-cut-conditions(c;e)))
⇒ {∀c:Cut(X;f). P[c]})
Proof
Definitions occuring in Statement :
add-cut-conditions: add-cut-conditions(c;e),
es-cut-add: c+e,
es-cut: Cut(X;f),
sys-antecedent: sys-antecedent(es;Sys),
es-E-interface: E(X),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
empty-fset: {},
linorder: Linorder(T;x,y.R[x; y]),
sq_stable: SqStable(P),
decidable: Dec(P),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
top: Top,
prop: ℙ,
guard: {T},
so_apply: x[s1;s2],
so_apply: x[s],
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
implies: P ⇒ Q,
or: P ∨ Q,
and: P ∧ Q,
function: x:A ─→ B[x],
universe: Type
Lemmas :
all_wf,
es-cut_wf,
es-E-interface_wf,
add-cut-conditions_wf,
es-cut-add_wf,
not_wf,
equal_wf,
assert_wf,
in-eclass_wf,
es-prior-interface_wf0,
es-interface-subtype_rel2,
es-E_wf,
event-ordering+_subtype,
event-ordering+_wf,
top_wf,
subtype_top,
empty-fset_wf-cut,
or_wf,
exists_wf,
linorder_wf,
decidable_wf,
sq_stable_wf,
sys-antecedent_wf,
eclass_wf,
fset-member_wf-cut,
eclass-val_wf2,
es-prior-interface_wf,
decidable__fset-member,
es-eq_wf-interface,
fset-closed_wf,
cons_wf,
es-interface-pred_wf2,
nil_wf,
fset-extensionality,
fset-union_wf,
fset-singleton_wf,
fset-member_witness,
fset-member_wf,
member-fset-union,
uiff_wf,
member-fset-singleton,
sq_stable_from_decidable,
decidable__fset-closed,
es-cut-add-at,
Id_wf,
es-loc_wf,
list_wf,
es-interface-predecessors-step,
iff_weakening_equal,
bool_cases,
subtype_base_sq,
bool_wf,
bool_subtype_base,
eqtt_to_assert,
eqff_to_assert,
assert_of_bnot,
es-cut-at_wf,
es-interface-predecessors_wf,
subtype_rel_list_set,
es-loc-prior-interface,
decidable__equal_int,
length_wf,
false_wf,
not-equal-2,
member_wf,
general-append-cancellation,
member-cut-add,
es-cut-induction-ordered,
isect_wf,
es-cut-induction-sq-stable
Latex:
\mforall{}[Info:Type]
\mforall{}es:EO+(Info). \mforall{}X:EClass(Top). \mforall{}f:sys-antecedent(es;X).
\mforall{}[P:Cut(X;f) {}\mrightarrow{} \mBbbP{}]
(((\mexists{}R:E(X) {}\mrightarrow{} E(X) {}\mrightarrow{} \mBbbP{}. (Linorder(E(X);x,y.R[x;y]) \mwedge{} (\mforall{}x,y:E(X). Dec(R[x;y]))))
\mvee{} (\mforall{}c:Cut(X;f). SqStable(P[c])))
{}\mRightarrow{} P[\{\}]
{}\mRightarrow{} (\mforall{}c:Cut(X;f). \mforall{}e:E(X). (P[c] {}\mRightarrow{} P[c+e] supposing add-cut-conditions(c;e)))
{}\mRightarrow{} \{\mforall{}c:Cut(X;f). P[c]\})
Date html generated:
2015_07_21-PM-04_03_41
Last ObjectModification:
2015_02_04-PM-06_08_29
Home
Index