Nuprl Lemma : list-match-aux_wf
∀[A,B:Type]. ∀[R:A ⟶ B ⟶ ℙ]. ∀[as:A List]. ∀[bs:B List]. ∀[used:ℤ List]. (list-match-aux(as;bs;used;a,b.R[a;b]) ∈ ℙ)
Proof
Definitions occuring in Statement :
list-match-aux: list-match-aux(L1;L2;used;a,b.R[a; b]),
list: T List,
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s1;s2],
member: t ∈ T,
function: x:A ⟶ B[x],
int: ℤ,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
list-match-aux: list-match-aux(L1;L2;used;a,b.R[a; b]),
so_lambda: λ2x.t[x],
prop: ℙ,
and: P ∧ Q,
subtype_rel: A ⊆r B,
so_apply: x[s1;s2],
int_seg: {i..j-},
uimplies: b supposing a,
guard: {T},
lelt: i ≤ j < k,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
not: ¬A,
implies: P ⇒ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
top: Top,
less_than: a < b,
squash: ↓T,
ge: i ≥ j ,
nat: ℕ,
so_apply: x[s]
Lemmas referenced :
sq_exists_wf,
int_seg_wf,
length_wf,
inject_wf,
all_wf,
not_wf,
l_member_wf,
select_wf,
int_seg_properties,
decidable__le,
full-omega-unsat,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_wf,
decidable__lt,
intformless_wf,
int_formula_prop_less_lemma,
non_neg_length,
lelt_wf,
length_wf_nat,
nat_properties,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
functionEquality,
natural_numberEquality,
cumulativity,
hypothesisEquality,
hypothesis,
because_Cache,
lambdaEquality,
productEquality,
functionExtensionality,
applyEquality,
intEquality,
setElimination,
rename,
independent_isectElimination,
productElimination,
dependent_functionElimination,
unionElimination,
approximateComputation,
independent_functionElimination,
dependent_pairFormation,
int_eqEquality,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
imageElimination,
dependent_set_memberEquality,
equalityTransitivity,
equalitySymmetry,
applyLambdaEquality,
axiomEquality,
universeEquality
Latex:
\mforall{}[A,B:Type]. \mforall{}[R:A {}\mrightarrow{} B {}\mrightarrow{} \mBbbP{}]. \mforall{}[as:A List]. \mforall{}[bs:B List]. \mforall{}[used:\mBbbZ{} List].
(list-match-aux(as;bs;used;a,b.R[a;b]) \mmember{} \mBbbP{})
Date html generated:
2018_05_21-PM-00_46_29
Last ObjectModification:
2018_05_19-AM-06_49_39
Theory : list_1
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