Nuprl Lemma : es-interface-equality-recursion
∀[Info,A:Type]. ∀[X,Y:EClass(A)].
X = Y ∈ EClass(A)
supposing ∀es:EO+(Info). ∀e:E.
((∀e':E. ((e' < e) ⇒ ((X es e') = (Y es e') ∈ bag(A)))) ⇒ ((X es e) = (Y es e) ∈ bag(A)))
Proof
Definitions occuring in Statement :
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-causl: (e < e'),
es-E: E,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
apply: f a,
universe: Type,
equal: s = t ∈ T,
bag: bag(T)
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
eclass: EClass(A[eo; e]),
all: ∀x:A. B[x],
subtype_rel: A ⊆r B,
prop: ℙ,
so_lambda: λ2x.t[x],
implies: P ⇒ Q,
so_apply: x[s],
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
strongwellfounded: SWellFounded(R[x; y]),
exists: ∃x:A. B[x],
nat: ℕ,
false: False,
ge: i ≥ j ,
satisfiable_int_formula: satisfiable_int_formula(fmla),
not: ¬A,
top: Top,
and: P ∧ Q,
guard: {T},
int_seg: {i..j-},
lelt: i ≤ j < k,
le: A ≤ B,
less_than': less_than'(a;b),
decidable: Dec(P),
or: P ∨ Q,
less_than: a < b,
squash: ↓T
Latex:
\mforall{}[Info,A:Type]. \mforall{}[X,Y:EClass(A)].
X = Y
supposing \mforall{}es:EO+(Info). \mforall{}e:E.
((\mforall{}e':E. ((e' < e) {}\mRightarrow{} ((X es e') = (Y es e')))) {}\mRightarrow{} ((X es e) = (Y es e)))
Date html generated:
2016_05_16-PM-10_26_46
Last ObjectModification:
2016_01_17-PM-07_30_45
Theory : event-ordering
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