Nuprl Lemma : length_mon_for_char
∀A:Type. ∀as:A List. (||as|| = (For{<ℤ+>} x ∈ as. 1) ∈ ℤ)
Proof
Definitions occuring in Statement :
mon_for: For{g} x ∈ as. f[x],
length: ||as||,
list: T List,
all: ∀x:A. B[x],
natural_number: $n,
int: ℤ,
universe: Type,
equal: s = t ∈ T,
int_add_grp: <ℤ+>
Definitions unfolded in proof :
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
int_add_grp: <ℤ+>,
grp_car: |g|,
pi1: fst(t),
so_apply: x[s],
implies: P ⇒ Q,
top: Top,
grp_id: e,
pi2: snd(t),
grp_op: *,
infix_ap: x f y,
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A,
and: P ∧ Q,
prop: ℙ
Lemmas referenced :
int_formula_prop_wf,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_term_value_add_lemma,
int_formula_prop_eq_lemma,
int_formula_prop_not_lemma,
int_formula_prop_and_lemma,
itermConstant_wf,
itermVar_wf,
itermAdd_wf,
intformeq_wf,
intformnot_wf,
intformand_wf,
satisfiable-full-omega-tt,
decidable__equal_int,
mon_for_cons_lemma,
length_of_cons_lemma,
mon_for_nil_lemma,
length_of_nil_lemma,
list_wf,
int_add_grp_wf,
mon_for_wf,
length_wf,
equal_wf,
list_induction
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
thin,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
sqequalRule,
lambdaEquality,
intEquality,
cumulativity,
hypothesis,
dependent_functionElimination,
applyEquality,
because_Cache,
natural_numberEquality,
independent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
rename,
unionElimination,
equalityTransitivity,
equalitySymmetry,
independent_isectElimination,
dependent_pairFormation,
int_eqEquality,
independent_pairFormation,
computeAll,
universeEquality
Latex:
\mforall{}A:Type. \mforall{}as:A List. (||as|| = (For\{<\mBbbZ{}+>\} x \mmember{} as. 1))
Date html generated:
2016_05_16-AM-07_36_28
Last ObjectModification:
2016_01_16-PM-11_13_06
Theory : list_2
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