Nuprl Lemma : es-interface-sum-non-neg
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[X:EClass(ℤ)]. ∀[e:E]. (0 ≤ Σ≤e(X)) supposing ∀e:E(X). (0 ≤ X(e))
Proof
Definitions occuring in Statement :
es-interface-sum: Σ≤e(X),
es-E-interface: E(X),
eclass-val: X(e),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
le: A ≤ B,
all: ∀x:A. B[x],
natural_number: $n,
int: ℤ,
universe: Type
Lemmas :
less_than_wf,
es-E_wf,
event-ordering+_subtype,
all_wf,
es-E-interface_wf,
es-interface-subtype_rel2,
event-ordering+_wf,
top_wf,
subtype_top,
le_wf,
eclass-val_wf,
assert_elim,
in-eclass_wf,
subtype_base_sq,
bool_wf,
bool_subtype_base,
eclass_wf,
es-local-prior-state-induction,
false_wf,
zero-le-nat,
add-nat,
nat_wf,
sq_stable__le,
es-locl_wf,
equal-wf-T-base,
assert_wf,
bnot_wf,
not_wf,
eqtt_to_assert,
uiff_transitivity,
eqff_to_assert,
assert_of_bnot,
es-local-prior-state_wf
Latex:
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[X:EClass(\mBbbZ{})]. \mforall{}[e:E]. (0 \mleq{} \mSigma{}\mleq{}e(X)) supposing \mforall{}e:E(X). (0 \mleq{} X(e))
Date html generated:
2015_07_21-PM-03_44_04
Last ObjectModification:
2015_01_27-PM-06_28_14
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