Nuprl Lemma : es-local-prior-state-induction
∀[Info,T:Type]. ∀[P:T ─→ ℙ].
∀es:EO+(Info)
∀[A:Type]
∀X:EClass(A). ∀base:T. ∀f:T ─→ A ─→ T. ∀e:E.
(P[base] ⇒ (∀x:T. ∀e':E(X). ((e' <loc e) ⇒ P[x] ⇒ P[f x X(e')])) ⇒ P[prior-state(f;base;X;e)])
Proof
Definitions occuring in Statement :
es-local-prior-state: prior-state(f;base;X;e),
es-E-interface: E(X),
eclass-val: X(e),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-locl: (e <loc e'),
es-E: E,
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s],
all: ∀x:A. B[x],
implies: P ⇒ Q,
apply: f a,
function: x:A ─→ B[x],
universe: Type
Lemmas :
event-ordering+_subtype,
all_wf,
es-E-interface_wf,
es-interface-subtype_rel2,
es-E_wf,
event-ordering+_wf,
top_wf,
es-locl_wf,
eclass-val_wf,
assert_elim,
in-eclass_wf,
subtype_base_sq,
bool_wf,
bool_subtype_base,
es-local-prior-state_wf,
es-prior-interface_wf1,
subtype_top,
equal-wf-T-base,
assert_wf,
bnot_wf,
not_wf,
eclass_wf,
eqtt_to_assert,
uiff_transitivity,
eqff_to_assert,
assert_of_bnot,
Id_wf,
es-loc-prior-interface,
es-loc_wf,
iff_weakening_equal,
es-prior-interface-causl,
eclass-val_wf2,
es-prior-interface_wf,
es-locl_transitivity2,
es-le_weakening
Latex:
\mforall{}[Info,T:Type]. \mforall{}[P:T {}\mrightarrow{} \mBbbP{}].
\mforall{}es:EO+(Info)
\mforall{}[A:Type]
\mforall{}X:EClass(A). \mforall{}base:T. \mforall{}f:T {}\mrightarrow{} A {}\mrightarrow{} T. \mforall{}e:E.
(P[base]
{}\mRightarrow{} (\mforall{}x:T. \mforall{}e':E(X). ((e' <loc e) {}\mRightarrow{} P[x] {}\mRightarrow{} P[f x X(e')]))
{}\mRightarrow{} P[prior-state(f;base;X;e)])
Date html generated:
2015_07_21-PM-03_42_25
Last ObjectModification:
2015_02_04-PM-06_11_32
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