Nuprl Lemma : es-interface-equality-prior-recursion
∀[Info,T:Type]. ∀[X,Y:EClass(T)].
X = Y ∈ EClass(T)
supposing ∀es:EO+(Info). ∀e:E. ((((X)' es e) = ((Y)' es e) ∈ bag(T)) ⇒ ((X es e) = (Y es e) ∈ bag(T)))
Proof
Definitions occuring in Statement :
es-prior-val: (X)',
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
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,
all: ∀x:A. B[x],
implies: P ⇒ Q,
prop: ℙ,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
eclass: EClass(A[eo; e]),
so_apply: x[s],
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
es-prior-val: (X)',
top: Top,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
ifthenelse: if b then t else f fi ,
bfalse: ff,
squash: ↓T,
true: True,
guard: {T},
rev_uimplies: rev_uimplies(P;Q),
iff: P ⇐⇒ Q,
in-eclass: e ∈b X,
rev_implies: P ⇐ Q,
nat: ℕ,
eclass-val: X(e),
cand: A c∧ B,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A
Latex:
\mforall{}[Info,T:Type]. \mforall{}[X,Y:EClass(T)].
X = Y supposing \mforall{}es:EO+(Info). \mforall{}e:E. ((((X)' es e) = ((Y)' es e)) {}\mRightarrow{} ((X es e) = (Y es e)))
Date html generated:
2016_05_17-AM-06_40_39
Last ObjectModification:
2016_01_17-PM-06_36_33
Theory : event-ordering
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