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
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
guard: {T},
so_lambda: λ2x.t[x],
member: t ∈ T,
so_apply: x[s1;s2],
subtype_rel: A ⊆r B,
so_apply: x[s],
prop: ℙ
Lemmas referenced :
RankEx4-induction,
set_wf,
RankEx4_wf,
all_wf,
true_wf,
RankEx4_Foo_wf
Rules used in proof :
cut,
lemma_by_obid,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
sqequalRule,
lambdaEquality,
hypothesisEquality,
applyEquality,
because_Cache,
independent_functionElimination,
unionEquality,
intEquality,
functionEquality,
decideEquality,
universeEquality,
cumulativity
Latex:
\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:
2016_05_16-AM-09_04_41
Last ObjectModification:
2015_12_28-PM-06_50_43
Theory : C-semantics
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