Nuprl Lemma : fpf-all-join-decl
∀[A:Type]
∀eq:EqDecider(A)
∀[P:x:A ─→ Type ─→ ℙ]
∀f,g:x:A fp-> Type.
(∀y∈dom(f). w=f(y) ⇒ P[y;w] ⇒ ∀y∈dom(g). w=g(y) ⇒ P[y;w] ⇒ ∀y∈dom(f ⊕ g). w=f ⊕ g(y) ⇒ P[y;w])
Proof
Definitions occuring in Statement :
fpf-all: ∀x∈dom(f). v=f(x) ⇒ P[x; v],
fpf-join: f ⊕ g,
fpf: a:A fp-> B[a],
deq: EqDecider(T),
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s1;s2],
all: ∀x:A. B[x],
implies: P ⇒ Q,
function: x:A ─→ B[x],
universe: Type
Lemmas :
fpf-join-dom2,
fpf-join-ap-sq,
assert_wf,
fpf-dom_wf,
fpf-join_wf,
top_wf,
subtype-fpf2,
subtype_top,
fpf-all_wf,
fpf_wf,
deq_wf,
bool_wf,
equal-wf-T-base,
bnot_wf,
not_wf,
eqtt_to_assert,
uiff_transitivity,
eqff_to_assert,
assert_of_bnot
\mforall{}[A:Type]
\mforall{}eq:EqDecider(A)
\mforall{}[P:x:A {}\mrightarrow{} Type {}\mrightarrow{} \mBbbP{}]
\mforall{}f,g:x:A fp-> Type.
(\mforall{}y\mmember{}dom(f). w=f(y) {}\mRightarrow{} P[y;w]
{}\mRightarrow{} \mforall{}y\mmember{}dom(g). w=g(y) {}\mRightarrow{} P[y;w]
{}\mRightarrow{} \mforall{}y\mmember{}dom(f \moplus{} g). w=f \moplus{} g(y) {}\mRightarrow{} P[y;w])
Date html generated:
2015_07_17-AM-11_14_00
Last ObjectModification:
2015_01_28-AM-07_41_57
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