Nuprl Lemma : es-fix-equal
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[X:EClass(Top)]. ∀[f:E(X) ─→ E(X)].
∀[e:E(X)]. uiff(f**(e) = e ∈ E;(f e) = e ∈ E) supposing ∀x:E(X). f x c≤ x
Proof
Definitions occuring in Statement :
es-E-interface: E(X),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-fix: f**(e),
es-causle: e c≤ e',
es-E: E,
uiff: uiff(P;Q),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
top: Top,
all: ∀x:A. B[x],
apply: f a,
function: x:A ─→ B[x],
universe: Type,
equal: s = t ∈ T
Lemmas :
all_wf,
es-causle_wf,
event-ordering+_subtype,
es-E-interface_wf,
eclass_wf,
top_wf,
es-E_wf,
event-ordering+_wf,
equal_wf,
sq_stable__uiff,
sq_stable__equal,
es-fix_wf2,
es-fix_property,
in-eclass_wf,
sq_stable__assert,
assert_wf,
and_wf,
eqof_wf,
es-eq_wf,
bool_wf,
equal-wf-T-base,
es-eq_wf-interface,
bnot_wf,
not_wf,
assert_elim,
subtype_base_sq,
bool_subtype_base,
uiff_transitivity,
eqtt_to_assert,
safe-assert-deq,
iff_transitivity,
iff_weakening_uiff,
eqff_to_assert,
assert_of_bnot
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[X:EClass(Top)]. \mforall{}[f:E(X) {}\mrightarrow{} E(X)].
\mforall{}[e:E(X)]. uiff(f**(e) = e;(f e) = e) supposing \mforall{}x:E(X). f x c\mleq{} x
Date html generated:
2015_07_17-PM-01_00_26
Last ObjectModification:
2015_01_27-PM-10_49_37
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