Nuprl Lemma : list_match-aux-nil
∀[bs:Top List]. ∀[used,R:Top]. list-match-aux([];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]),
nil: [],
list: T List,
uall: ∀[x:A]. B[x],
top: Top,
so_apply: x[s1;s2]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
list-match-aux: list-match-aux(L1;L2;used;a,b.R[a; b]),
sq_exists: ∃x:A [B[x]],
member: t ∈ T,
int_seg: {i..j-},
lelt: i ≤ j < k,
and: P ∧ Q,
uimplies: b supposing a,
not: ¬A,
implies: P ⇒ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
all: ∀x:A. B[x],
top: Top,
prop: ℙ,
select: L[n],
nil: [],
it: ⋅,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
cand: A c∧ B,
inject: Inj(A;B;f),
guard: {T},
decidable: Dec(P),
or: P ∨ Q,
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
so_apply: x[s]
Lemmas referenced :
length_of_nil_lemma,
full-omega-unsat,
intformand_wf,
intformless_wf,
itermVar_wf,
itermConstant_wf,
intformle_wf,
int_formula_prop_and_lemma,
int_formula_prop_less_lemma,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_wf,
lelt_wf,
length_wf,
top_wf,
int_seg_wf,
stuck-spread,
base_wf,
int_seg_properties,
decidable__equal_int,
intformnot_wf,
intformeq_wf,
int_formula_prop_not_lemma,
int_formula_prop_eq_lemma,
equal_wf,
inject_wf,
all_wf,
not_wf,
l_member_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
dependent_set_memberFormation,
sqequalRule,
cut,
introduction,
extract_by_obid,
hypothesis,
lambdaEquality,
sqequalHypSubstitution,
setElimination,
thin,
rename,
dependent_set_memberEquality,
hypothesisEquality,
productElimination,
independent_pairFormation,
isectElimination,
natural_numberEquality,
independent_isectElimination,
approximateComputation,
independent_functionElimination,
dependent_pairFormation,
int_eqEquality,
intEquality,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
because_Cache,
baseClosed,
lambdaFormation,
equalityTransitivity,
equalitySymmetry,
applyLambdaEquality,
unionElimination,
productEquality,
functionExtensionality,
applyEquality
Latex:
\mforall{}[bs:Top List]. \mforall{}[used,R:Top]. list-match-aux([];bs;used;a,b.R[a;b])
Date html generated:
2018_05_21-PM-00_46_41
Last ObjectModification:
2018_05_19-AM-06_49_49
Theory : list_1
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