Nuprl Lemma : mklist-prepend1
∀[f:Top]. ∀[m:ℕ]. (mklist(1 + m;f) ~ [f 0] @ mklist(m;λi.(f (1 + i))))
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
,
lambda: λx.A[x]
,
add: n + m
,
natural_number: $n
,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x]
,
member: t ∈ T
,
nat: ℕ
,
implies: P
⇒ Q
,
false: False
,
ge: i ≥ j
,
uimplies: b supposing a
,
not: ¬A
,
satisfiable_int_formula: satisfiable_int_formula(fmla)
,
exists: ∃x:A. B[x]
,
all: ∀x:A. B[x]
,
top: Top
,
and: P ∧ Q
,
prop: ℙ
,
append: as @ bs
,
so_lambda: so_lambda(x,y,z.t[x; y; z])
,
so_apply: x[s1;s2;s3]
,
mklist: mklist(n;f)
,
decidable: Dec(P)
,
or: P ∨ Q
,
sq_type: SQType(T)
,
guard: {T}
,
bool: 𝔹
,
unit: Unit
,
it: ⋅
,
btrue: tt
,
uiff: uiff(P;Q)
,
ifthenelse: if b then t else f fi
,
bfalse: ff
,
bnot: ¬bb
,
assert: ↑b
,
rev_implies: P
⇐ Q
,
iff: P
⇐⇒ Q
Lemmas referenced :
nat_properties,
full-omega-unsat,
intformand_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
intformless_wf,
istype-int,
int_formula_prop_and_lemma,
istype-void,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_less_lemma,
int_formula_prop_wf,
ge_wf,
istype-less_than,
list_ind_cons_lemma,
list_ind_nil_lemma,
primrec0_lemma,
primrec1_lemma,
subtract-1-ge-0,
subtype_base_sq,
int_subtype_base,
decidable__equal_int,
intformnot_wf,
intformeq_wf,
itermAdd_wf,
itermSubtract_wf,
int_formula_prop_not_lemma,
int_formula_prop_eq_lemma,
int_term_value_add_lemma,
int_term_value_subtract_lemma,
istype-nat,
istype-top,
primrec-unroll,
lt_int_wf,
eqtt_to_assert,
assert_of_lt_int,
eqff_to_assert,
bool_cases_sqequal,
bool_wf,
bool_subtype_base,
assert-bnot,
iff_weakening_uiff,
assert_wf,
less_than_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
setElimination,
rename,
intWeakElimination,
Error :lambdaFormation_alt,
natural_numberEquality,
independent_isectElimination,
approximateComputation,
independent_functionElimination,
Error :dependent_pairFormation_alt,
Error :lambdaEquality_alt,
int_eqEquality,
dependent_functionElimination,
Error :isect_memberEquality_alt,
voidElimination,
sqequalRule,
independent_pairFormation,
Error :universeIsType,
axiomSqEquality,
Error :functionIsTypeImplies,
Error :inhabitedIsType,
instantiate,
cumulativity,
intEquality,
because_Cache,
unionElimination,
equalityTransitivity,
equalitySymmetry,
Error :isectIsTypeImplies,
addEquality,
equalityElimination,
productElimination,
Error :equalityIstype,
promote_hyp
Latex:
\mforall{}[f:Top]. \mforall{}[m:\mBbbN{}]. (mklist(1 + m;f) \msim{} [f 0] @ mklist(m;\mlambda{}i.(f (1 + i))))
Date html generated:
2019_06_20-PM-01_31_39
Last ObjectModification:
2019_02_06-PM-03_51_15
Theory : list_1
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