Nuprl Lemma : prior-val-induction3
∀[Info,T:Type].
∀es:EO+(Info). ∀X:EClass(T).
∀[P:E(X) ─→ T ─→ ℙ]
((∀e:E(X). (P[e;X(e)] supposing ¬↑e ∈b (X)' ∧ P[prior(X)(e);(X)'(e)] ⇒ P[e;X(e)] supposing ↑e ∈b (X)'))
⇒ (∀e:E(X). P[e;X(e)]))
Proof
Definitions occuring in Statement :
es-prior-val: (X)',
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[s1;s2],
all: ∀x:A. B[x],
not: ¬A,
implies: P ⇒ Q,
and: P ∧ Q,
function: x:A ─→ B[x],
universe: Type
Lemmas :
prior-interface-induction,
eclass_wf,
es-E_wf,
event-ordering+_subtype,
event-ordering+_wf,
es-E-interface_wf,
es-interface-subtype_rel2,
top_wf,
eclass-val_wf,
assert_elim,
in-eclass_wf,
subtype_base_sq,
bool_wf,
bool_subtype_base,
assert_wf,
es-prior-interface_wf1,
subtype_top,
is-prior-val-iff-prior-interface,
es-prior-val_wf,
not_wf,
assert_witness,
eclass-val_wf2,
es-prior-interface_wf,
es-E-interface-property,
eqtt_to_assert,
bag_only_single_lemma,
eqff_to_assert,
bfalse_wf,
and_wf,
equal_wf,
bnot_wf,
btrue_neq_bfalse,
bool_cases_sqequal,
all_wf
Latex:
\mforall{}[Info,T:Type].
\mforall{}es:EO+(Info). \mforall{}X:EClass(T).
\mforall{}[P:E(X) {}\mrightarrow{} T {}\mrightarrow{} \mBbbP{}]
((\mforall{}e:E(X)
(P[e;X(e)] supposing \mneg{}\muparrow{}e \mmember{}\msubb{} (X)'
\mwedge{} P[prior(X)(e);(X)'(e)] {}\mRightarrow{} P[e;X(e)] supposing \muparrow{}e \mmember{}\msubb{} (X)'))
{}\mRightarrow{} (\mforall{}e:E(X). P[e;X(e)]))
Date html generated:
2015_07_21-PM-03_24_08
Last ObjectModification:
2015_01_27-PM-06_48_14
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