Nuprl Lemma : mklist-add1
∀[n:ℕ]. ∀[f:Top].  (mklist(n + 1;f) ~ mklist(n;f) @ [f n])
Proof
Definitions occuring in Statement : 
mklist: mklist(n;f)
, 
append: as @ bs
, 
cons: [a / b]
, 
nil: []
, 
nat: ℕ
, 
uall: ∀[x:A]. B[x]
, 
top: Top
, 
apply: f a
, 
add: n + m
, 
natural_number: $n
, 
sqequal: s ~ t
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
mklist: mklist(n;f)
, 
nat: ℕ
, 
top: Top
, 
all: ∀x:A. B[x]
, 
implies: P 
⇒ Q
, 
bool: 𝔹
, 
unit: Unit
, 
it: ⋅
, 
btrue: tt
, 
uiff: uiff(P;Q)
, 
and: P ∧ Q
, 
uimplies: b supposing a
, 
ifthenelse: if b then t else f fi 
, 
ge: i ≥ j 
, 
satisfiable_int_formula: satisfiable_int_formula(fmla)
, 
exists: ∃x:A. B[x]
, 
false: False
, 
not: ¬A
, 
prop: ℙ
, 
bfalse: ff
, 
or: P ∨ Q
, 
sq_type: SQType(T)
, 
guard: {T}
, 
bnot: ¬bb
, 
assert: ↑b
Lemmas referenced : 
top_wf, 
nat_wf, 
primrec-unroll, 
eq_int_wf, 
bool_wf, 
eqtt_to_assert, 
assert_of_eq_int, 
nat_properties, 
satisfiable-full-omega-tt, 
intformand_wf, 
intformeq_wf, 
itermAdd_wf, 
itermVar_wf, 
itermConstant_wf, 
intformle_wf, 
int_formula_prop_and_lemma, 
int_formula_prop_eq_lemma, 
int_term_value_add_lemma, 
int_term_value_var_lemma, 
int_term_value_constant_lemma, 
int_formula_prop_le_lemma, 
int_formula_prop_wf, 
eqff_to_assert, 
equal_wf, 
bool_cases_sqequal, 
subtype_base_sq, 
bool_subtype_base, 
assert-bnot, 
neg_assert_of_eq_int, 
add-subtract-cancel
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation, 
introduction, 
cut, 
hypothesis, 
sqequalAxiom, 
extract_by_obid, 
sqequalRule, 
sqequalHypSubstitution, 
isect_memberEquality, 
isectElimination, 
thin, 
hypothesisEquality, 
because_Cache, 
addEquality, 
setElimination, 
rename, 
natural_numberEquality, 
voidElimination, 
voidEquality, 
lambdaFormation, 
unionElimination, 
equalityElimination, 
equalityTransitivity, 
equalitySymmetry, 
productElimination, 
independent_isectElimination, 
dependent_pairFormation, 
lambdaEquality, 
int_eqEquality, 
intEquality, 
dependent_functionElimination, 
independent_pairFormation, 
computeAll, 
promote_hyp, 
instantiate, 
cumulativity, 
independent_functionElimination
Latex:
\mforall{}[n:\mBbbN{}].  \mforall{}[f:Top].    (mklist(n  +  1;f)  \msim{}  mklist(n;f)  @  [f  n])
Date html generated:
2017_04_17-AM-07_42_10
Last ObjectModification:
2017_02_27-PM-04_14_44
Theory : list_1
Home
Index