Nuprl Lemma : prior-interface-induction
∀[Info,T:Type].
∀es:EO+(Info). ∀X:EClass(T).
∀[P:E(X) ─→ ℙ]
((∀e:E(X). (P[e] supposing ¬↑e ∈b prior(X) ∧ P[prior(X)(e)] ⇒ P[e] supposing ↑e ∈b prior(X))) ⇒ (∀e:E(X). P[e]))
Proof
Definitions occuring in Statement :
es-prior-interface: prior(X),
es-E-interface: E(X),
eclass-val: X(e),
in-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
assert: ↑b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s],
all: ∀x:A. B[x],
not: ¬A,
implies: P ⇒ Q,
and: P ∧ Q,
function: x:A ─→ B[x],
universe: Type
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,
assert_wf,
in-eclass_wf,
es-interface-subtype_rel2,
es-E_wf,
event-ordering+_wf,
top_wf,
equal_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,
decidable__assert,
es-prior-interface_wf1,
subtype_top,
es-E-interface_wf,
es-prior-interface-causl,
es-E-interface-property,
eclass-val_wf2,
es-prior-interface_wf,
es-prior-interface_wf0,
eclass_wf,
eclass-val_wf,
assert_functionality_wrt_uiff,
squash_wf,
true_wf
Latex:
\mforall{}[Info,T:Type].
\mforall{}es:EO+(Info). \mforall{}X:EClass(T).
\mforall{}[P:E(X) {}\mrightarrow{} \mBbbP{}]
((\mforall{}e:E(X). (P[e] supposing \mneg{}\muparrow{}e \mmember{}\msubb{} prior(X) \mwedge{} P[prior(X)(e)] {}\mRightarrow{} P[e] supposing \muparrow{}e \mmember{}\msubb{} prior(X)))
{}\mRightarrow{} (\mforall{}e:E(X). P[e]))
Date html generated:
2015_07_21-PM-02_48_15
Last ObjectModification:
2015_01_27-PM-07_36_16
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