Nuprl Lemma : free-from-atom-fpf-ap
∀[a:Atom1]. ∀[A:Type]. ∀[eq:EqDecider(A)]. ∀[B:A ⟶ 𝕌']. ∀[f:x:A fp-> B[x]].
∀[x:A]. (a#f(x):B[x]) supposing ((↑x ∈ dom(f)) and a#x:A) supposing a#f:x:A fp-> B[x]
Proof
Definitions occuring in Statement :
fpf-ap: f(x),
fpf-dom: x ∈ dom(f),
fpf: a:A fp-> B[a],
deq: EqDecider(T),
free-from-atom: a#x:T,
atom: Atom$n,
assert: ↑b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
so_apply: x[s],
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
member: t ∈ T,
all: ∀x:A. B[x],
implies: P ⇒ Q,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
top: Top,
prop: ℙ,
iff: P ⇐⇒ Q,
and: P ∧ Q,
fpf-ap: f(x),
fpf-domain: fpf-domain(f),
fpf: a:A fp-> B[a],
pi2: snd(t),
pi1: fst(t),
squash: ↓T,
true: True
Latex:
\mforall{}[a:Atom1]. \mforall{}[A:Type]. \mforall{}[eq:EqDecider(A)]. \mforall{}[B:A {}\mrightarrow{} \mBbbU{}']. \mforall{}[f:x:A fp-> B[x]].
\mforall{}[x:A]. (a\#f(x):B[x]) supposing ((\muparrow{}x \mmember{} dom(f)) and a\#x:A) supposing a\#f:x:A fp-> B[x]
Date html generated:
2016_05_16-AM-11_42_38
Last ObjectModification:
2016_01_17-PM-03_48_51
Theory : event-ordering
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