Nuprl Lemma : cut-order-induction
∀[Info:Type]
∀es:EO+(Info). ∀X:EClass(Top). ∀f:sys-antecedent(es;X).
∀[P:E(X) ─→ ℙ]. ((∀b:E(X). ((∀a:E(X). (P[a]) supposing ((¬(a = b ∈ E(X))) and a ≤(X;f) b)) ⇒ P[b])) ⇒ (∀e:E(X). P[\000Ce]))
Proof
Definitions occuring in Statement :
cut-order: a ≤(X;f) b,
sys-antecedent: sys-antecedent(es;Sys),
es-E-interface: E(X),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
top: Top,
prop: ℙ,
so_apply: x[s],
all: ∀x:A. B[x],
not: ¬A,
implies: P ⇒ Q,
function: x:A ─→ B[x],
universe: Type,
equal: s = t ∈ T
Lemmas :
es-causl-swellfnd,
event-ordering+_subtype,
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,
cut-order_witness,
not_wf,
equal_wf,
cut-order_wf,
all_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,
es-E-interface_wf,
isect_wf,
sys-antecedent_wf,
eclass_wf,
top_wf,
es-E_wf,
event-ordering+_wf,
cut-order-causle,
assert_elim,
in-eclass_wf,
subtype_base_sq,
bool_wf,
bool_subtype_base,
assert_wf
Latex:
\mforall{}[Info:Type]
\mforall{}es:EO+(Info). \mforall{}X:EClass(Top). \mforall{}f:sys-antecedent(es;X).
\mforall{}[P:E(X) {}\mrightarrow{} \mBbbP{}]
((\mforall{}b:E(X). ((\mforall{}a:E(X). (P[a]) supposing ((\mneg{}(a = b)) and a \mleq{}(X;f) b)) {}\mRightarrow{} P[b])) {}\mRightarrow{} (\mforall{}e:E(X). P[e\000C]))
Date html generated:
2015_07_21-PM-04_06_13
Last ObjectModification:
2015_01_27-PM-05_47_26
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