Nuprl Lemma : fpf-join-dom-sq
∀[A:Type]. ∀[eq:EqDecider(A)]. ∀[f,g:a:A fp-> Top]. ∀[x:A]. (x ∈ dom(f ⊕ g) ~ x ∈ dom(f) ∨bx ∈ dom(g))
Proof
Definitions occuring in Statement :
fpf-join: f ⊕ g,
fpf-dom: x ∈ dom(f),
fpf: a:A fp-> B[a],
deq: EqDecider(T),
bor: p ∨bq,
uall: ∀[x:A]. B[x],
top: Top,
universe: Type,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
fpf: a:A fp-> B[a],
fpf-dom: x ∈ dom(f),
fpf-join: f ⊕ g,
pi1: fst(t),
all: ∀x:A. B[x],
prop: ℙ,
sq_type: SQType(T),
implies: P ⇒ Q,
guard: {T},
so_lambda: λ2x.t[x],
so_apply: x[s],
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
or: P ∨ Q,
not: ¬A,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
bfalse: ff,
cand: A c∧ B,
false: False
Latex:
\mforall{}[A:Type]. \mforall{}[eq:EqDecider(A)]. \mforall{}[f,g:a:A fp-> Top]. \mforall{}[x:A].
(x \mmember{} dom(f \moplus{} g) \msim{} x \mmember{} dom(f) \mvee{}\msubb{}x \mmember{} dom(g))
Date html generated:
2016_05_16-AM-11_10_43
Last ObjectModification:
2015_12_29-AM-09_18_45
Theory : event-ordering
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