Nuprl Lemma : C_TYPE-definition
∀[A:Type]. ∀[R:A ⟶ C_TYPE() ⟶ ℙ].
({x:A| R[x;C_Void()]}
⇒ {x:A| R[x;C_Int()]}
⇒ (∀fields:(Atom × C_TYPE()) List. ((∀u∈fields.let u1,u2 = u in {x:A| R[x;u2]} ) ⇒ {x:A| R[x;C_Struct(fields)]} ))
⇒ (∀length:ℕ. ∀elems:C_TYPE(). ({x:A| R[x;elems]} ⇒ {x:A| R[x;C_Array(length;elems)]} ))
⇒ (∀to:C_TYPE(). ({x:A| R[x;to]} ⇒ {x:A| R[x;C_Pointer(to)]} ))
⇒ {∀v:C_TYPE(). {x:A| R[x;v]} })
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(),
l_all: (∀x∈L.P[x]),
list: T List,
nat: ℕ,
uall: ∀[x:A]. B[x],
prop: ℙ,
guard: {T},
so_apply: x[s1;s2],
all: ∀x:A. B[x],
implies: P ⇒ Q,
set: {x:A| B[x]} ,
function: x:A ⟶ B[x],
spread: spread def,
product: x:A × B[x],
atom: Atom,
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 :
C_TYPE-induction,
set_wf,
C_TYPE_wf,
all_wf,
C_Pointer_wf,
nat_wf,
C_Array_wf,
list_wf,
l_all_wf2,
l_member_wf,
C_Struct_wf,
C_Int_wf,
C_Void_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,
functionEquality,
universeEquality,
productEquality,
atomEquality,
spreadEquality,
setElimination,
rename,
setEquality,
cumulativity
Latex:
\mforall{}[A:Type]. \mforall{}[R:A {}\mrightarrow{} C\_TYPE() {}\mrightarrow{} \mBbbP{}].
(\{x:A| R[x;C\_Void()]\}
{}\mRightarrow{} \{x:A| R[x;C\_Int()]\}
{}\mRightarrow{} (\mforall{}fields:(Atom \mtimes{} C\_TYPE()) List
((\mforall{}u\mmember{}fields.let u1,u2 = u in \{x:A| R[x;u2]\} ) {}\mRightarrow{} \{x:A| R[x;C\_Struct(fields)]\} ))
{}\mRightarrow{} (\mforall{}length:\mBbbN{}. \mforall{}elems:C\_TYPE(). (\{x:A| R[x;elems]\} {}\mRightarrow{} \{x:A| R[x;C\_Array(length;elems)]\} ))
{}\mRightarrow{} (\mforall{}to:C\_TYPE(). (\{x:A| R[x;to]\} {}\mRightarrow{} \{x:A| R[x;C\_Pointer(to)]\} ))
{}\mRightarrow{} \{\mforall{}v:C\_TYPE(). \{x:A| R[x;v]\} \})
Date html generated:
2016_05_16-AM-08_45_17
Last ObjectModification:
2015_12_28-PM-06_57_57
Theory : C-semantics
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