Nuprl Lemma : C_TYPE_ind_wf
∀[A:Type]. ∀[R:A ⟶ C_TYPE() ⟶ ℙ]. ∀[v:C_TYPE()]. ∀[Void:{x:A| R[x;C_Void()]} ]. ∀[Int:{x:A| R[x;C_Int()]} ].
∀[Struct:fields:((Atom × C_TYPE()) List)
⟶ (∀u∈fields.let u1,u2 = u
in {x:A| R[x;u2]} )
⟶ {x:A| R[x;C_Struct(fields)]} ]. ∀[Array:length:ℕ
⟶ elems:C_TYPE()
⟶ {x:A| R[x;elems]}
⟶ {x:A| R[x;C_Array(length;elems)]} ].
∀[Pointer:to:C_TYPE() ⟶ {x:A| R[x;to]} ⟶ {x:A| R[x;C_Pointer(to)]} ].
(C_TYPE_ind(v
Void=>Void
Int=>Int
Struct(fields)=>rec1.Struct[fields;rec1]
Array(length,elems)=>rec2.Array[length;elems;rec2]
Pointer(to)=>rec3.Pointer[to;rec3]) ∈ {x:A| R[x;v]} )
Proof
Definitions occuring in Statement :
C_TYPE_ind: C_TYPE_ind,
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,
so_apply: x[s1;s2;s3],
so_apply: x[s1;s2],
member: t ∈ T,
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],
member: t ∈ T,
C_TYPE_ind: C_TYPE_ind,
so_apply: x[s1;s2],
so_apply: x[s1;s2;s3],
C_TYPE-definition,
C_TYPE-induction,
uniform-comp-nat-induction,
C_TYPE-ext,
eq_atom: x =a y,
bool_cases_sqequal,
eqff_to_assert,
any: any x,
btrue: tt,
bfalse: ff,
it: ⋅,
top: Top,
all: ∀x:A. B[x],
implies: P ⇒ Q,
has-value: (a)↓,
so_lambda: so_lambda(x,y,z,w.t[x; y; z; w]),
so_apply: x[s1;s2;s3;s4],
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a,
strict4: strict4(F),
and: P ∧ Q,
prop: ℙ,
guard: {T},
or: P ∨ Q,
squash: ↓T,
so_lambda: λ2x y.t[x; y],
subtype_rel: A ⊆r B
Lemmas referenced :
C_TYPE-definition,
C_TYPE-induction,
uniform-comp-nat-induction,
C_TYPE-ext,
bool_cases_sqequal,
eqff_to_assert,
guard_wf,
all_wf,
C_Pointer_wf,
C_Array_wf,
nat_wf,
C_Struct_wf,
set_wf,
l_member_wf,
l_all_wf2,
list_wf,
C_Int_wf,
C_Void_wf,
C_TYPE_wf,
lifting-strict-spread,
base_wf,
lifting-strict-atom_eq,
is-exception_wf,
has-value_wf_base,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
isect_memberEquality,
voidElimination,
voidEquality,
thin,
lemma_by_obid,
hypothesis,
lambdaFormation,
because_Cache,
sqequalSqle,
divergentSqle,
callbyvalueDecide,
sqequalHypSubstitution,
unionEquality,
unionElimination,
sqleReflexivity,
equalityEquality,
equalityTransitivity,
equalitySymmetry,
hypothesisEquality,
dependent_functionElimination,
independent_functionElimination,
decideExceptionCases,
axiomSqleEquality,
exceptionSqequal,
baseApply,
closedConclusion,
baseClosed,
isectElimination,
independent_isectElimination,
independent_pairFormation,
inrFormation,
imageMemberEquality,
imageElimination,
inlFormation,
callbyvalueApply,
applyExceptionCases,
instantiate,
extract_by_obid,
applyEquality,
lambdaEquality,
isectEquality,
functionEquality,
cumulativity,
universeEquality,
setEquality,
setElimination,
rename,
productEquality,
atomEquality,
productElimination,
independent_pairEquality,
dependent_set_memberEquality,
axiomEquality,
spreadEquality
Latex:
\mforall{}[A:Type]. \mforall{}[R:A {}\mrightarrow{} C\_TYPE() {}\mrightarrow{} \mBbbP{}]. \mforall{}[v:C\_TYPE()]. \mforall{}[Void:\{x:A| R[x;C\_Void()]\} ].
\mforall{}[Int:\{x:A| R[x;C\_Int()]\} ]. \mforall{}[Struct:fields:((Atom \mtimes{} C\_TYPE()) List)
{}\mrightarrow{} (\mforall{}u\mmember{}fields.let u1,u2 = u
in \{x:A| R[x;u2]\} )
{}\mrightarrow{} \{x:A| R[x;C\_Struct(fields)]\} ].
\mforall{}[Array:length:\mBbbN{} {}\mrightarrow{} elems:C\_TYPE() {}\mrightarrow{} \{x:A| R[x;elems]\} {}\mrightarrow{} \{x:A| R[x;C\_Array(length;elems)]\} ].
\mforall{}[Pointer:to:C\_TYPE() {}\mrightarrow{} \{x:A| R[x;to]\} {}\mrightarrow{} \{x:A| R[x;C\_Pointer(to)]\} ].
(C\_TYPE\_ind(v
Void=>Void
Int=>Int
Struct(fields)=>rec1.Struct[fields;rec1]
Array(length,elems)=>rec2.Array[length;elems;rec2]
Pointer(to)=>rec3.Pointer[to;rec3]) \mmember{} \{x:A| R[x;v]\} )
Date html generated:
2016_05_16-AM-08_45_22
Last ObjectModification:
2016_01_17-AM-09_44_21
Theory : C-semantics
Home
Index