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
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
es-E-interface: E(X),
member: t ∈ T,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
sq_type: SQType(T),
guard: {T},
assert: ↑b,
ifthenelse: if b then t else f fi ,
btrue: tt,
true: True,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
top: Top,
prop: ℙ,
so_lambda: λ2x.t[x],
and: P ∧ Q,
so_apply: x[s],
strongwellfounded: SWellFounded(R[x; y]),
exists: ∃x:A. B[x],
int_seg: {i..j-},
lelt: i ≤ j < k,
satisfiable_int_formula: satisfiable_int_formula(fmla),
false: False,
not: ¬A,
decidable: Dec(P),
or: P ∨ Q,
le: A ≤ B,
less_than': less_than'(a;b),
nat: ℕ,
ge: i ≥ j ,
less_than: a < b,
squash: ↓T,
uiff: uiff(P;Q),
rev_uimplies: rev_uimplies(P;Q)
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:
2016_05_16-PM-11_58_40
Last ObjectModification:
2016_01_17-PM-07_01_22
Theory : event-ordering
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