Nuprl Lemma : es-fwd-propagation-via-unique
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[T:Type]. ∀[X,Y:EClass(T)]. ∀[f,g:E(X) ─→ E(Y)].
(f = g ∈ (E(X) ─→ E(Y))) supposing
(Surj(E(X);E(Y);g) and
Surj(E(X);E(Y);f) and
g:X ⇒ Y:T and
f:X ⇒ Y:T and
(∀y1,y2:E(Y). (loc(y1) = loc(y2) ∈ Id)) and
(∀x1,x2:E(X). (loc(x1) = loc(x2) ∈ Id)))
Proof
Definitions occuring in Statement :
es-fwd-propagation-via: f:X ⇒ Y:T,
es-E-interface: E(X),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-loc: loc(e),
Id: Id,
surject: Surj(A;B;f),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
function: x:A ─→ B[x],
universe: Type,
equal: s = t ∈ T
Lemmas :
es-causl-swellfnd,
event-ordering+_subtype,
nat_properties,
less_than_transitivity1,
less_than_irreflexivity,
ge_wf,
less_than_wf,
int_seg_wf,
int_seg_subtype-nat,
decidable__le,
subtract_wf,
false_wf,
not-ge-2,
less-iff-le,
condition-implies-le,
minus-one-mul,
zero-add,
minus-add,
minus-minus,
add-associates,
add-swap,
add-commutes,
add_functionality_wrt_le,
add-zero,
le-add-cancel,
decidable__equal_int,
subtype_rel-int_seg,
le_weakening,
int_seg_properties,
le_wf,
nat_wf,
zero-le-nat,
lelt_wf,
es-causl_wf,
es-locl-total,
es-E-interface-property,
assert_wf,
in-eclass_wf,
equal_wf,
decidable__lt,
not-equal-2,
le-add-cancel-alt,
not-le-2,
sq_stable__le,
add-mul-special,
zero-mul,
surject_wf,
es-E-interface_wf,
es-interface-subtype_rel2,
es-E_wf,
event-ordering+_wf,
top_wf,
es-fwd-propagation-via_wf,
all_wf,
Id_wf,
es-loc_wf,
eclass_wf,
assert_elim,
subtype_base_sq,
bool_wf,
bool_subtype_base,
and_wf,
es-locl_transitivity2,
es-le_weakening,
es-le_weakening_eq,
es-locl_irreflexivity,
es-causl_weakening
Latex:
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[T:Type]. \mforall{}[X,Y:EClass(T)]. \mforall{}[f,g:E(X) {}\mrightarrow{} E(Y)].
(f = g) supposing
(Surj(E(X);E(Y);g) and
Surj(E(X);E(Y);f) and
g:X {}\mRightarrow{} Y:T and
f:X {}\mRightarrow{} Y:T and
(\mforall{}y1,y2:E(Y). (loc(y1) = loc(y2))) and
(\mforall{}x1,x2:E(X). (loc(x1) = loc(x2))))
Date html generated:
2015_07_21-PM-03_27_19
Last ObjectModification:
2015_01_27-PM-06_49_03
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