Nuprl Lemma : fpf-compatible-singles-iff
∀[A:Type]. ∀[eq:EqDecider(A)]. ∀[B:A ⟶ Type]. ∀[x,y:A]. ∀[v:B[x]]. ∀[u:B[y]].
uiff(x : v || y : u;v = u ∈ B[x] supposing x = y ∈ A)
Proof
Definitions occuring in Statement :
fpf-single: x : v,
fpf-compatible: f || g,
deq: EqDecider(T),
uiff: uiff(P;Q),
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 :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
fpf-compatible: f || g,
all: ∀x:A. B[x],
top: Top,
implies: P ⇒ Q,
cand: A c∧ B,
rev_uimplies: rev_uimplies(P;Q),
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
subtype_rel: A ⊆r B
Latex:
\mforall{}[A:Type]. \mforall{}[eq:EqDecider(A)]. \mforall{}[B:A {}\mrightarrow{} Type]. \mforall{}[x,y:A]. \mforall{}[v:B[x]]. \mforall{}[u:B[y]].
uiff(x : v || y : u;v = u supposing x = y)
Date html generated:
2016_05_16-AM-11_30_13
Last ObjectModification:
2015_12_29-AM-09_25_53
Theory : event-ordering
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