Nuprl Lemma : C_TYPE-induction2
∀[P:C_TYPE() ─→ ℙ]
(P[C_Void()]
⇒ P[C_Int()]
⇒ (∀fields:(Atom × C_TYPE()) List. ((∀i:ℕ||fields||. P[snd(fields[i])]) ⇒ P[C_Struct(fields)]))
⇒ (∀length:ℕ. ∀elems:C_TYPE(). (P[elems] ⇒ P[C_Array(length;elems)]))
⇒ (∀to:C_TYPE(). (P[to] ⇒ P[C_Pointer(to)]))
⇒ {∀x:C_TYPE(). P[x]})
Proof
Definitions occuring in Statement :
C_Pointer: C_Pointer(to),
C_Array: C_Array(length;elems),
C_Struct: C_Struct(fields),
C_Int: C_Int(),
C_Void: C_Void(),
C_TYPE: C_TYPE(),
select: L[n],
length: ||as||,
list: T List,
int_seg: {i..j-},
nat: ℕ,
uall: ∀[x:A]. B[x],
prop: ℙ,
guard: {T},
so_apply: x[s],
pi2: snd(t),
all: ∀x:A. B[x],
implies: P ⇒ Q,
function: x:A ─→ B[x],
product: x:A × B[x],
natural_number: $n,
atom: Atom
Lemmas :
C_TYPE-induction,
l_all_wf2,
C_TYPE_wf,
l_member_wf,
list_wf,
all_wf,
int_seg_wf,
length_wf,
select_wf,
sq_stable__le,
C_Struct_wf,
C_Int_wf,
C_Void_wf
\mforall{}[P:C\_TYPE() {}\mrightarrow{} \mBbbP{}]
(P[C\_Void()]
{}\mRightarrow{} P[C\_Int()]
{}\mRightarrow{} (\mforall{}fields:(Atom \mtimes{} C\_TYPE()) List. ((\mforall{}i:\mBbbN{}||fields||. P[snd(fields[i])]) {}\mRightarrow{} P[C\_Struct(fields)]))
{}\mRightarrow{} (\mforall{}length:\mBbbN{}. \mforall{}elems:C\_TYPE(). (P[elems] {}\mRightarrow{} P[C\_Array(length;elems)]))
{}\mRightarrow{} (\mforall{}to:C\_TYPE(). (P[to] {}\mRightarrow{} P[C\_Pointer(to)]))
{}\mRightarrow{} \{\mforall{}x:C\_TYPE(). P[x]\})
Date html generated:
2015_07_17-AM-07_42_52
Last ObjectModification:
2015_01_27-AM-09_47_01
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