Nuprl Lemma : decidable__squash-list-match-ext
∀[A,B:Type]. ∀[R:A ⟶ B ⟶ ℙ].
((∀a:A. ∀b:B. Dec(R[a;b])) ⇒ (∀as:A List. ∀bs:B List. Dec(↓list-match(as;bs;a,b.R[a;b]))))
Proof
Definitions occuring in Statement :
list-match: list-match(L1;L2;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],
universe: Type
Definitions unfolded in proof :
member: t ∈ T,
ifthenelse: if b then t else f fi ,
it: ⋅,
btrue: tt,
let: let,
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
unit: Unit,
sq_type: SQType(T),
all: ∀x:A. B[x],
implies: P ⇒ Q,
guard: {T},
decidable__squash-list-match,
decidable__squash-list-match-aux-ext
Lemmas referenced :
decidable__squash-list-match,
subtype_base_sq,
unit_wf2,
unit_subtype_base,
trivial-equal,
decidable__squash-list-match-aux-ext
Rules used in proof :
introduction,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
cut,
instantiate,
extract_by_obid,
hypothesis,
sqequalRule,
thin,
sqequalHypSubstitution,
equalityTransitivity,
equalitySymmetry,
isectElimination,
cumulativity,
independent_isectElimination,
axiomEquality,
natural_numberEquality,
dependent_functionElimination,
independent_functionElimination,
because_Cache
Latex:
\mforall{}[A,B:Type]. \mforall{}[R:A {}\mrightarrow{} B {}\mrightarrow{} \mBbbP{}].
((\mforall{}a:A. \mforall{}b:B. Dec(R[a;b])) {}\mRightarrow{} (\mforall{}as:A List. \mforall{}bs:B List. Dec(\mdownarrow{}list-match(as;bs;a,b.R[a;b]))))
Date html generated:
2018_05_21-PM-00_50_17
Last ObjectModification:
2018_05_19-AM-06_51_35
Theory : list_1
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