Nuprl Lemma : decidable__squash-list-match-aux-ext
∀[A,B:Type]. ∀[R:A ⟶ B ⟶ ℙ].
((∀a:A. ∀b:B. Dec(R[a;b])) ⇒ (∀bs:B List. ∀as:A List. ∀used:ℤ List. Dec(↓list-match-aux(as;bs;used;a,b.R[a;b]))))
Proof
Definitions occuring in Statement :
list-match-aux: list-match-aux(L1;L2;used;a,b.R[a; b]),
list: T List,
decidable: Dec(P),
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s1;s2],
all: ∀x:A. B[x],
squash: ↓T,
implies: P ⇒ Q,
function: x:A ⟶ B[x],
int: ℤ,
universe: Type
Definitions unfolded in proof :
member: t ∈ T,
ifthenelse: if b then t else f fi ,
decidable__squash-list-match-aux,
list_induction,
decidable_functionality,
decidable__exists_int_seg,
decidable__and2,
decidable__not,
decidable__assert,
iff_preserves_decidability,
decidable__implies,
decidable__false,
decidable__and,
any: any x,
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
Lemmas referenced :
decidable__squash-list-match-aux,
lifting-strict-decide,
strict4-decide,
lifting-strict-callbyvalue,
list_induction,
decidable_functionality,
decidable__exists_int_seg,
decidable__and2,
decidable__not,
decidable__assert,
iff_preserves_decidability,
decidable__implies,
decidable__false,
decidable__and
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
Latex:
\mforall{}[A,B:Type]. \mforall{}[R:A {}\mrightarrow{} B {}\mrightarrow{} \mBbbP{}].
((\mforall{}a:A. \mforall{}b:B. Dec(R[a;b]))
{}\mRightarrow{} (\mforall{}bs:B List. \mforall{}as:A List. \mforall{}used:\mBbbZ{} List. Dec(\mdownarrow{}list-match-aux(as;bs;used;a,b.R[a;b]))))
Date html generated:
2018_05_21-PM-00_47_46
Last ObjectModification:
2018_05_19-AM-06_50_45
Theory : list_1
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