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
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
so_lambda: λ2x y.t[x; y],
subtype_rel: A ⊆r B,
so_apply: x[s1;s2],
implies: P ⇒ Q,
prop: ℙ,
uimplies: b supposing a,
top: Top,
so_lambda: λ2x.t[x],
es-E-interface: E(X),
sq_type: SQType(T),
guard: {T},
assert: ↑b,
ifthenelse: if b then t else f fi ,
btrue: tt,
true: True,
so_apply: x[s],
and: P ∧ Q,
cand: A c∧ B,
not: ¬A,
false: False,
uiff: uiff(P;Q),
rev_uimplies: rev_uimplies(P;Q),
eclass-val: X(e),
es-prior-val: (X)',
bool: 𝔹,
unit: Unit,
it: ⋅,
bfalse: ff,
bnot: ¬bb,
exists: ∃x:A. B[x],
or: P ∨ Q
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:
2016_05_17-AM-06_39_31
Last ObjectModification:
2015_12_29-AM-00_32_22
Theory : event-ordering
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