Nuprl Lemma : fpf-rename_wf
∀[A,C:Type]. ∀[B:A ⟶ Type]. ∀[D:C ⟶ Type]. ∀[eq:EqDecider(C)]. ∀[r:A ⟶ C]. ∀[f:a:A fp-> B[a]].
rename(r;f) ∈ c:C fp-> D[c] supposing ∀a:A. (D[r a] = B[a] ∈ Type)
Proof
Definitions occuring in Statement :
fpf-rename: rename(r;f),
fpf: a:A fp-> B[a],
deq: EqDecider(T),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
so_apply: x[s],
all: ∀x:A. B[x],
member: t ∈ T,
apply: f a,
function: x:A ⟶ B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
fpf: a:A fp-> B[a],
fpf-rename: rename(r;f),
pi1: fst(t),
pi2: snd(t),
prop: ℙ,
so_apply: x[s],
so_lambda: λ2x.t[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
subtype_rel: A ⊆r B,
deq: EqDecider(T),
iff: P ⇐⇒ Q,
and: P ∧ Q,
exists: ∃x:A. B[x],
cand: A c∧ B,
eqof: eqof(d),
uiff: uiff(P;Q),
rev_uimplies: rev_uimplies(P;Q)
Latex:
\mforall{}[A,C:Type]. \mforall{}[B:A {}\mrightarrow{} Type]. \mforall{}[D:C {}\mrightarrow{} Type]. \mforall{}[eq:EqDecider(C)]. \mforall{}[r:A {}\mrightarrow{} C]. \mforall{}[f:a:A fp-> B[a]].
rename(r;f) \mmember{} c:C fp-> D[c] supposing \mforall{}a:A. (D[r a] = B[a])
Date html generated:
2016_05_16-AM-11_25_31
Last ObjectModification:
2015_12_29-AM-09_37_14
Theory : event-ordering
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