Nuprl Lemma : fpf-compatible-singles
∀[A:Type]. ∀[eq:EqDecider(A)]. ∀[B:A ⟶ Type]. ∀[x,y:A]. ∀[v:B[x]]. ∀[u:B[y]].
x : v || y : u supposing (x = y ∈ A) ⇒ (v = u ∈ B[x])
Proof
Definitions occuring in Statement :
fpf-single: x : v,
fpf-compatible: f || g,
deq: EqDecider(T),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
so_apply: x[s],
implies: P ⇒ Q,
function: x:A ⟶ B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
member: t ∈ T,
uall: ∀[x:A]. B[x],
so_lambda: λ2x.t[x],
so_apply: x[s],
subtype_rel: A ⊆r B,
top: Top,
and: P ∧ Q,
prop: ℙ,
implies: P ⇒ Q,
uimplies: b supposing a,
fpf-compatible: f || g,
all: ∀x:A. B[x],
fpf-single: x : v,
fpf-dom: x ∈ dom(f),
pi1: fst(t),
deq: EqDecider(T),
or: P ∨ Q,
false: False,
eqof: eqof(d),
iff: P ⇐⇒ Q,
uiff: uiff(P;Q),
assert: ↑b,
ifthenelse: if b then t else f fi ,
bfalse: ff,
rev_implies: P ⇐ Q,
guard: {T}
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]].
x : v || y : u supposing (x = y) {}\mRightarrow{} (v = u)
Date html generated:
2016_05_16-AM-11_29_15
Last ObjectModification:
2015_12_29-AM-09_37_20
Theory : event-ordering
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