Nuprl Lemma : mklist_add1
∀[n:ℕ+]. ∀[f:Top]. (mklist(n;f) ~ mklist(n - 1;f) @ [f (n - 1)])
Proof
Definitions occuring in Statement :
mklist: mklist(n;f),
append: as @ bs,
cons: [a / b],
nil: [],
nat_plus: ℕ+,
uall: ∀[x:A]. B[x],
top: Top,
apply: f a,
subtract: 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_plus: 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 ,
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_plus_wf,
primrec-unroll,
eq_int_wf,
bool_wf,
eqtt_to_assert,
assert_of_eq_int,
nat_plus_properties,
satisfiable-full-omega-tt,
intformand_wf,
intformeq_wf,
itermVar_wf,
itermConstant_wf,
intformless_wf,
int_formula_prop_and_lemma,
int_formula_prop_eq_lemma,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_formula_prop_less_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
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,
setElimination,
rename,
voidElimination,
voidEquality,
natural_numberEquality,
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{}\msupplus{}]. \mforall{}[f:Top]. (mklist(n;f) \msim{} mklist(n - 1;f) @ [f (n - 1)])
Date html generated:
2017_04_17-AM-07_42_19
Last ObjectModification:
2017_02_27-PM-04_14_49
Theory : list_1
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