Nuprl Lemma : fpf-inv-rename_wf
∀[A,C:Type]. ∀[B:A ⟶ Type]. ∀[D:C ⟶ Type]. ∀[rinv:C ⟶ (A?)]. ∀[r:A ⟶ C]. ∀[f:c:C fp-> D[c]].
(fpf-inv-rename(r;rinv;f) ∈ a:A fp-> B[a]) supposing ((∀a:A. (D[r a] = B[a] ∈ Type)) and inv-rel(A;C;r;rinv))
Proof
Definitions occuring in Statement :
fpf-inv-rename: fpf-inv-rename(r;rinv;f),
fpf: a:A fp-> B[a],
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
so_apply: x[s],
all: ∀x:A. B[x],
unit: Unit,
member: t ∈ T,
apply: f a,
function: x:A ⟶ B[x],
union: left + right,
universe: Type,
equal: s = t ∈ T,
inv-rel: inv-rel(A;B;f;finv)
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
fpf-inv-rename: fpf-inv-rename(r;rinv;f),
fpf: a:A fp-> B[a],
pi1: fst(t),
pi2: snd(t),
prop: ℙ,
so_apply: x[s],
so_lambda: λ2x.t[x],
all: ∀x:A. B[x],
isl: isl(x),
compose: f o g,
subtype_rel: A ⊆r B,
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
exists: ∃x:A. B[x],
cand: A c∧ B,
inv-rel: inv-rel(A;B;f;finv),
outl: outl(x),
assert: ↑b,
ifthenelse: if b then t else f fi ,
btrue: tt,
bfalse: ff,
false: False
Latex:
\mforall{}[A,C:Type]. \mforall{}[B:A {}\mrightarrow{} Type]. \mforall{}[D:C {}\mrightarrow{} Type]. \mforall{}[rinv:C {}\mrightarrow{} (A?)]. \mforall{}[r:A {}\mrightarrow{} C]. \mforall{}[f:c:C fp-> D[c]].
(fpf-inv-rename(r;rinv;f) \mmember{} a:A fp-> B[a]) supposing
((\mforall{}a:A. (D[r a] = B[a])) and
inv-rel(A;C;r;rinv))
Date html generated:
2016_05_16-AM-11_26_41
Last ObjectModification:
2015_12_29-AM-09_23_54
Theory : event-ordering
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