Nuprl Lemma : upto_decomp2
∀[n:ℕ+]. (upto(n) ~ [0 / map(λi.(i + 1);upto(n - 1))])
Proof
Definitions occuring in Statement :
upto: upto(n),
map: map(f;as),
cons: [a / b],
nat_plus: ℕ+,
uall: ∀[x:A]. B[x],
lambda: λx.A[x],
subtract: n - m,
add: n + m,
natural_number: $n,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
int_seg: {i..j-},
lelt: i ≤ j < k,
and: P ∧ Q,
le: A ≤ B,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
prop: ℙ,
nat_plus: ℕ+,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
top: Top,
upto: upto(n),
from-upto: [n, m),
ifthenelse: if b then t else f fi ,
lt_int: i <z j,
btrue: tt,
cons: [a / b],
bfalse: ff,
nil: [],
it: ⋅,
append: as @ bs,
so_lambda: so_lambda(x,y,z.t[x; y; z]),
so_apply: x[s1;s2;s3]
Lemmas referenced :
list_ind_nil_lemma,
list_ind_cons_lemma,
nat_plus_wf,
lelt_wf,
int_formula_prop_wf,
int_term_value_var_lemma,
int_term_value_add_lemma,
int_term_value_constant_lemma,
int_formula_prop_less_lemma,
int_formula_prop_not_lemma,
int_formula_prop_and_lemma,
itermVar_wf,
itermAdd_wf,
itermConstant_wf,
intformless_wf,
intformnot_wf,
intformand_wf,
satisfiable-full-omega-tt,
decidable__lt,
nat_plus_properties,
false_wf,
nat_plus_subtype_nat,
upto_decomp
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
applyEquality,
hypothesis,
sqequalRule,
dependent_set_memberEquality,
natural_numberEquality,
independent_pairFormation,
lambdaFormation,
setElimination,
rename,
dependent_functionElimination,
addEquality,
unionElimination,
independent_isectElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
computeAll,
sqequalAxiom
Latex:
\mforall{}[n:\mBbbN{}\msupplus{}]. (upto(n) \msim{} [0 / map(\mlambda{}i.(i + 1);upto(n - 1))])
Date html generated:
2016_05_14-PM-02_04_00
Last ObjectModification:
2016_01_15-AM-08_05_40
Theory : list_1
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