Nuprl Lemma : list_2_decomp
∀[T:Type]. ∀[z:T List]. z = [z[0]; z[1]] ∈ (T List) supposing ||z|| = 2 ∈ ℕ
Proof
Definitions occuring in Statement :
select: L[n],
length: ||as||,
cons: [a / b],
nil: [],
list: T List,
nat: ℕ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
natural_number: $n,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
all: ∀x:A. B[x],
or: P ∨ Q,
select: L[n],
nil: [],
it: ⋅,
so_lambda: λ2x y.t[x; y],
top: Top,
so_apply: x[s1;s2],
nat: ℕ,
guard: {T},
prop: ℙ,
ge: i ≥ j ,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
cons: [a / b],
subtract: n - m,
le: A ≤ B,
and: P ∧ Q,
implies: P ⇒ Q,
not: ¬A
Lemmas referenced :
list_wf,
length_wf_nat,
nat_wf,
equal-wf-T-base,
int_term_value_add_lemma,
int_term_value_var_lemma,
int_formula_prop_le_lemma,
int_formula_prop_and_lemma,
itermAdd_wf,
itermVar_wf,
intformle_wf,
intformand_wf,
non_neg_length,
nil_wf,
cons_wf,
length_of_cons_lemma,
product_subtype_list,
int_formula_prop_wf,
int_term_value_constant_lemma,
int_formula_prop_eq_lemma,
itermConstant_wf,
intformeq_wf,
satisfiable-full-omega-tt,
le_wf,
nat_properties,
base_wf,
stuck-spread,
length_of_nil_lemma,
list-cases
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
hypothesisEquality,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
dependent_functionElimination,
unionElimination,
sqequalRule,
baseClosed,
independent_isectElimination,
lambdaFormation,
isect_memberEquality,
voidElimination,
voidEquality,
equalityTransitivity,
equalitySymmetry,
applyEquality,
lambdaEquality,
setElimination,
rename,
setEquality,
intEquality,
natural_numberEquality,
dependent_pairFormation,
computeAll,
promote_hyp,
hypothesis_subsumption,
productElimination,
because_Cache,
int_eqEquality,
independent_pairFormation,
axiomEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[z:T List]. z = [z[0]; z[1]] supposing ||z|| = 2
Date html generated:
2016_05_14-PM-03_00_27
Last ObjectModification:
2016_01_15-AM-07_24_03
Theory : list_1
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