Nuprl Lemma : RankEx4-definition
∀[A:Type]. ∀[R:A ─→ RankEx4() ─→ ℙ].
((∀foo:ℤ + RankEx4(). (case foo of inl(u) => True | inr(u1) => {x:A| R[x;u1]} ⇒ {x:A| R[x;RankEx4_Foo(foo)]} ))
⇒ {∀v:RankEx4(). {x:A| R[x;v]} })
Proof
Definitions occuring in Statement :
RankEx4_Foo: RankEx4_Foo(foo),
RankEx4: RankEx4(),
uall: ∀[x:A]. B[x],
prop: ℙ,
guard: {T},
so_apply: x[s1;s2],
all: ∀x:A. B[x],
implies: P ⇒ Q,
true: True,
set: {x:A| B[x]} ,
function: x:A ─→ B[x],
decide: case b of inl(x) => s[x] | inr(y) => t[y],
union: left + right,
int: ℤ,
universe: Type
Lemmas :
RankEx4-induction,
set_wf,
all_wf,
RankEx4_wf,
true_wf,
RankEx4_Foo_wf
\mforall{}[A:Type]. \mforall{}[R:A {}\mrightarrow{} RankEx4() {}\mrightarrow{} \mBbbP{}].
((\mforall{}foo:\mBbbZ{} + RankEx4()
(case foo of inl(u) => True | inr(u1) => \{x:A| R[x;u1]\} {}\mRightarrow{} \{x:A| R[x;RankEx4\_Foo(foo)]\} ))
{}\mRightarrow{} \{\mforall{}v:RankEx4(). \{x:A| R[x;v]\} \})
Date html generated:
2015_07_17-AM-07_51_16
Last ObjectModification:
2015_01_27-AM-09_36_10
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