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
Lemmas :
assert_wf,
fpf-dom_wf,
subtype-fpf2,
top_wf,
subtype_top,
free-from-atom_wf,
fpf_wf,
deq_wf,
member-fpf-domain,
l_member_wf,
fpf-domain_wf,
set_wf,
equal_wf,
list_wf
\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:
2015_07_17-AM-11_19_21
Last ObjectModification:
2015_01_28-AM-07_36_47
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