Nuprl Lemma : fpf-normalize-ap
∀[A:Type]. ∀[eq:EqDecider(A)]. ∀[B:A ⟶ Type]. ∀[g:x:A fp-> B[x]]. ∀[x:A].
fpf-normalize(eq;g)(x) = g(x) ∈ B[x] supposing ↑x ∈ dom(g)
Proof
Definitions occuring in Statement :
fpf-normalize: fpf-normalize(eq;g),
fpf-ap: f(x),
fpf-dom: x ∈ dom(f),
fpf: a:A fp-> B[a],
deq: EqDecider(T),
assert: ↑b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
so_apply: x[s],
function: x:A ⟶ B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
fpf: a:A fp-> B[a],
fpf-ap: f(x),
fpf-normalize: fpf-normalize(eq;g),
pi2: snd(t),
pi1: fst(t),
fpf-empty: ⊗,
fpf-single: x : v,
fpf-join: f ⊕ g,
append: as @ bs,
all: ∀x:A. B[x],
so_lambda: so_lambda(x,y,z.t[x; y; z]),
member: t ∈ T,
top: Top,
so_apply: x[s1;s2;s3],
fpf-cap: f(x)?z,
fpf-dom: x ∈ dom(f),
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a,
prop: ℙ,
implies: P ⇒ Q,
nat: ℕ,
false: False,
ge: i ≥ j ,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
not: ¬A,
and: P ∧ Q,
or: P ∨ Q,
cons: [a / b],
colength: colength(L),
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
guard: {T},
decidable: Dec(P),
nil: [],
it: ⋅,
sq_type: SQType(T),
less_than: a < b,
squash: ↓T,
less_than': less_than'(a;b),
deq-member: x ∈b L,
assert: ↑b,
ifthenelse: if b then t else f fi ,
bfalse: ff,
deq: EqDecider(T),
bool: 𝔹,
unit: Unit,
btrue: tt,
eqof: eqof(d),
uiff: uiff(P;Q),
bor: p ∨bq,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Latex:
\mforall{}[A:Type]. \mforall{}[eq:EqDecider(A)]. \mforall{}[B:A {}\mrightarrow{} Type]. \mforall{}[g:x:A fp-> B[x]]. \mforall{}[x:A].
fpf-normalize(eq;g)(x) = g(x) supposing \muparrow{}x \mmember{} dom(g)
Date html generated:
2016_05_16-AM-11_37_39
Last ObjectModification:
2016_01_17-PM-03_53_04
Theory : event-ordering
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