Nuprl Lemma : mklist-eq
∀[n:ℕ]. ∀[f,g:ℕ ⟶ Base]. mklist(n;f) ~ mklist(n;g) supposing ∀[i:ℕn]. (f i ~ g i)
Proof
Definitions occuring in Statement :
mklist: mklist(n;f),
int_seg: {i..j-},
nat: ℕ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
apply: f a,
function: x:A ⟶ B[x],
natural_number: $n,
base: Base,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
member: t ∈ T,
nat: ℕ,
implies: P ⇒ Q,
false: False,
ge: i ≥ j ,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
not: ¬A,
all: ∀x:A. B[x],
top: Top,
and: P ∧ Q,
prop: ℙ,
le: A ≤ B,
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
guard: {T},
so_apply: x[s],
mklist: mklist(n;f),
less_than': less_than'(a;b),
decidable: Dec(P),
or: P ∨ Q,
sq_type: SQType(T),
int_seg: {i..j-},
lelt: i ≤ j < k,
uiff: uiff(P;Q),
subtract: n - m,
less_than: a < b
Lemmas referenced :
int_seg_properties,
add-member-int_seg1,
add-member-int_seg2,
lelt_wf,
subtype_rel_self,
mklist-prepend1,
le_wf,
int_term_value_add_lemma,
int_formula_prop_eq_lemma,
itermAdd_wf,
intformeq_wf,
decidable__equal_int,
int_subtype_base,
subtype_base_sq,
int_term_value_subtract_lemma,
int_formula_prop_not_lemma,
itermSubtract_wf,
intformnot_wf,
subtract_wf,
decidable__le,
false_wf,
int_seg_subtype_nat,
primrec0_lemma,
base_wf,
nat_wf,
less_than_irreflexivity,
less_than_transitivity1,
sqequal-wf-base,
int_seg_wf,
uall_wf,
less_than_wf,
ge_wf,
int_formula_prop_wf,
int_formula_prop_less_lemma,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_and_lemma,
intformless_wf,
itermVar_wf,
itermConstant_wf,
intformle_wf,
intformand_wf,
satisfiable-full-omega-tt,
nat_properties
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
thin,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
hypothesis,
setElimination,
rename,
intWeakElimination,
lambdaFormation,
natural_numberEquality,
independent_isectElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
sqequalRule,
independent_pairFormation,
computeAll,
independent_functionElimination,
sqequalAxiom,
productElimination,
applyEquality,
because_Cache,
functionEquality,
sqequalIntensionalEquality,
unionElimination,
instantiate,
equalityTransitivity,
equalitySymmetry,
dependent_set_memberEquality,
cumulativity,
addEquality
Latex:
\mforall{}[n:\mBbbN{}]. \mforall{}[f,g:\mBbbN{} {}\mrightarrow{} Base]. mklist(n;f) \msim{} mklist(n;g) supposing \mforall{}[i:\mBbbN{}n]. (f i \msim{} g i)
Date html generated:
2016_05_14-PM-01_45_38
Last ObjectModification:
2016_01_15-AM-08_22_29
Theory : list_1
Home
Index