Nuprl Lemma : wellfounded-llex-ext
∀[A:Type]. ∀[<:A ⟶ A ⟶ ℙ].
((∀a,b:A. SqStable(<[a;b]))
⇒ WellFnd{i}(A;a,b.<[a;b])
⇒ WellFnd{i}(Des(A;a,b.<[a;b]);L1,L2.L1 llex(A;a,b.<[a;b]) L2))
Proof
Definitions occuring in Statement :
llex: llex(A;a,b.<[a; b]),
Des: Des(A;a,b.<[a; b]),
wellfounded: WellFnd{i}(A;x,y.R[x; y]),
sq_stable: SqStable(P),
uall: ∀[x:A]. B[x],
prop: ℙ,
infix_ap: x f y,
so_apply: x[s1;s2],
all: ∀x:A. B[x],
implies: P ⇒ Q,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
member: t ∈ T,
btrue: tt,
it: ⋅,
bfalse: ff,
spreadn: let a,b,c,d,e = u in v[a; b; c; d; e],
spreadn: spread4,
wellfounded-llex,
list-cases,
any: any x,
llex-append1,
decidable__lt,
colist-cases,
iff_weakening_equal,
iseg_select,
decidable__le,
decidable__squash,
decidable__and,
decidable__less_than',
colist-ext,
list_induction,
nil_iseg,
cons_iseg,
decidable__not,
decidable_functionality,
squash_elim,
sq_stable_from_decidable,
decidable__implies,
decidable__false,
iff_preserves_decidability,
sq_stable__from_stable,
stable__from_decidable,
uall: ∀[x:A]. B[x],
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],
top: Top,
so_apply: x[s],
uimplies: b supposing a,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
length: ||as||,
list_ind: list_ind,
nil: [],
all: ∀x:A. B[x],
implies: P ⇒ Q,
has-value: (a)↓,
prop: ℙ
Lemmas referenced :
wellfounded-llex,
lifting-strict-decide,
strict4-decide,
lifting-strict-isaxiom,
lifting-strict-spread,
lifting-strict-less,
strict4-spread,
top_wf,
equal_wf,
has-value_wf_base,
is-exception_wf,
list-cases,
llex-append1,
decidable__lt,
colist-cases,
iff_weakening_equal,
iseg_select,
decidable__le,
decidable__squash,
decidable__and,
decidable__less_than',
colist-ext,
list_induction,
nil_iseg,
cons_iseg,
decidable__not,
decidable_functionality,
squash_elim,
sq_stable_from_decidable,
decidable__implies,
decidable__false,
iff_preserves_decidability,
sq_stable__from_stable,
stable__from_decidable
Rules used in proof :
introduction,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
cut,
instantiate,
extract_by_obid,
hypothesis,
sqequalRule,
thin,
sqequalHypSubstitution,
equalityTransitivity,
equalitySymmetry,
isectElimination,
baseClosed,
isect_memberEquality,
voidElimination,
voidEquality,
independent_isectElimination,
lambdaFormation,
sqequalSqle,
divergentSqle,
callbyvalueSpread,
productEquality,
productElimination,
sqleReflexivity,
hypothesisEquality,
dependent_functionElimination,
independent_functionElimination,
spreadExceptionCases,
axiomSqleEquality,
exceptionSqequal,
baseApply,
closedConclusion
Latex:
\mforall{}[A:Type]. \mforall{}[<:A {}\mrightarrow{} A {}\mrightarrow{} \mBbbP{}].
((\mforall{}a,b:A. SqStable(<[a;b]))
{}\mRightarrow{} WellFnd\{i\}(A;a,b.<[a;b])
{}\mRightarrow{} WellFnd\{i\}(Des(A;a,b.<[a;b]);L1,L2.L1 llex(A;a,b.<[a;b]) L2))
Date html generated:
2018_05_21-PM-07_20_05
Last ObjectModification:
2018_05_19-PM-04_47_37
Theory : general
Home
Index