Nuprl Lemma : fpf-sub-set
∀[A:Type]. ∀[P:A ⟶ ℙ]. ∀[B:A ⟶ Type]. ∀[eq:EqDecider(A)]. ∀[f,g:a:{a:A| P[a]} fp-> B[a]]. f ⊆ g supposing f ⊆ g
Proof
Definitions occuring in Statement :
fpf-sub: f ⊆ g,
fpf: a:A fp-> B[a],
deq: EqDecider(T),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s],
set: {x:A| B[x]} ,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
member: t ∈ T,
so_lambda: λ2x.t[x],
so_apply: x[s],
subtype_rel: A ⊆r B,
implies: P ⇒ Q,
prop: ℙ,
fpf-sub: f ⊆ g,
all: ∀x:A. B[x],
fpf: a:A fp-> B[a],
fpf-dom: x ∈ dom(f),
pi1: fst(t),
iff: P ⇐⇒ Q,
and: P ∧ Q,
l_member: (x ∈ l),
exists: ∃x:A. B[x],
nat: ℕ,
ge: i ≥ j ,
cand: A c∧ B,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
false: False,
not: ¬A,
top: Top,
squash: ↓T
Latex:
\mforall{}[A:Type]. \mforall{}[P:A {}\mrightarrow{} \mBbbP{}]. \mforall{}[B:A {}\mrightarrow{} Type]. \mforall{}[eq:EqDecider(A)]. \mforall{}[f,g:a:\{a:A| P[a]\} fp-> B[a]].
f \msubseteq{} g supposing f \msubseteq{} g
Date html generated:
2016_05_16-AM-11_06_26
Last ObjectModification:
2016_01_17-PM-03_47_37
Theory : event-ordering
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