Nuprl Lemma : fpf-all-single
∀[A:Type]
∀eq:EqDecider(A)
∀[B:A ─→ Type]. ∀[P:x:A ─→ B[x] ─→ ℙ]. ∀x:A. ∀v:B[x]. (∀y∈dom(x : v). w=x : v(y) ⇒ P[y;w] ⇐⇒ P[x;v])
Proof
Definitions occuring in Statement :
fpf-all: ∀x∈dom(f). v=f(x) ⇒ P[x; v],
fpf-single: x : v,
deq: EqDecider(T),
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s1;s2],
so_apply: x[s],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
function: x:A ─→ B[x],
universe: Type
Lemmas :
deq_member_cons_lemma,
deq_member_nil_lemma,
deq_wf,
false_wf,
iff_transitivity,
assert_wf,
bor_wf,
eqof_wf,
bfalse_wf,
or_wf,
equal_wf,
iff_weakening_uiff,
assert_of_bor,
safe-assert-deq,
member_wf,
all_wf,
subtype_rel_self,
subtype_rel_wf,
and_wf
\mforall{}[A:Type]
\mforall{}eq:EqDecider(A)
\mforall{}[B:A {}\mrightarrow{} Type]. \mforall{}[P:x:A {}\mrightarrow{} B[x] {}\mrightarrow{} \mBbbP{}].
\mforall{}x:A. \mforall{}v:B[x]. (\mforall{}y\mmember{}dom(x : v). w=x : v(y) {}\mRightarrow{} P[y;w] \mLeftarrow{}{}\mRightarrow{} P[x;v])
Date html generated:
2015_07_17-AM-11_13_53
Last ObjectModification:
2015_01_28-AM-07_45_45
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