Nuprl Lemma : prior-val-induction2
∀[Info,T:Type].
∀es:EO+(Info). ∀X:EClass(T).
∀[P:Id ─→ T ─→ ℙ]
((∀e:E(X). (P[loc(e);X(e)] supposing ¬↑e ∈b (X)' ∧ P[loc(e);(X)'(e)] ⇒ P[loc(e);X(e)] supposing ↑e ∈b (X)'))
⇒ (∀e:E(X). P[loc(e);X(e)]))
Proof
Definitions occuring in Statement :
es-prior-val: (X)',
es-E-interface: E(X),
eclass-val: X(e),
in-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-loc: loc(e),
Id: Id,
assert: ↑b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s1;s2],
all: ∀x:A. B[x],
not: ¬A,
implies: P ⇒ Q,
and: P ∧ Q,
function: x:A ─→ B[x],
universe: Type
Lemmas :
es-E-interface_wf,
es-interface-subtype_rel2,
es-E_wf,
event-ordering+_subtype,
event-ordering+_wf,
top_wf,
all_wf,
not_wf,
assert_wf,
in-eclass_wf,
es-prior-val_wf,
es-loc_wf,
eclass-val_wf,
assert_elim,
subtype_base_sq,
bool_wf,
bool_subtype_base,
Id_wf,
eclass_wf,
decidable__assert,
es-causl-swellfnd,
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,
nat_wf,
zero-le-nat,
lelt_wf,
es-causl_wf,
equal_wf,
int_seg_subtype-nat,
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,
set_wf,
less_than_wf,
primrec-wf2,
decidable__le,
not-le-2,
sq_stable__le,
add-zero,
add-mul-special,
zero-mul,
prior-val-val,
atom2_subtype_base
Latex:
\mforall{}[Info,T:Type].
\mforall{}es:EO+(Info). \mforall{}X:EClass(T).
\mforall{}[P:Id {}\mrightarrow{} T {}\mrightarrow{} \mBbbP{}]
((\mforall{}e:E(X)
(P[loc(e);X(e)] supposing \mneg{}\muparrow{}e \mmember{}\msubb{} (X)'
\mwedge{} P[loc(e);(X)'(e)] {}\mRightarrow{} P[loc(e);X(e)] supposing \muparrow{}e \mmember{}\msubb{} (X)'))
{}\mRightarrow{} (\mforall{}e:E(X). P[loc(e);X(e)]))
Date html generated:
2015_07_21-PM-03_23_53
Last ObjectModification:
2015_07_16-AM-10_05_07
Home
Index