Nuprl Lemma : ml-int-vec-add-sq
∀[as,bs:ℤ List]. (ml-int-vec-add(as;bs) ~ as + bs)
Proof
Definitions occuring in Statement :
ml-int-vec-add: ml-int-vec-add(as;bs),
int-vec-add: as + bs,
list: T List,
uall: ∀[x:A]. B[x],
int: ℤ,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
nat: ℕ,
implies: P ⇒ Q,
false: False,
ge: i ≥ j ,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
not: ¬A,
top: Top,
and: P ∧ Q,
prop: ℙ,
subtype_rel: A ⊆r B,
guard: {T},
or: P ∨ Q,
ml-int-vec-add: ml-int-vec-add(as;bs),
ml_apply: f(x),
callbyvalueall: callbyvalueall,
evalall: evalall(t),
nil: [],
it: ⋅,
ifthenelse: if b then t else f fi ,
bor: p ∨bq,
null: null(as),
btrue: tt,
int-vec-add: as + bs,
sq_type: SQType(T),
cons: [a / b],
colength: colength(L),
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
so_lambda: λ2x.t[x],
so_apply: x[s],
decidable: Dec(P),
less_than: a < b,
squash: ↓T,
less_than': less_than'(a;b),
bfalse: ff,
spreadcons: spreadcons
Lemmas referenced :
nat_properties,
satisfiable-full-omega-tt,
intformand_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
intformless_wf,
int_formula_prop_and_lemma,
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,
less_than_wf,
list_wf,
equal-wf-base,
nat_wf,
list_subtype_base,
int_subtype_base,
less_than_transitivity1,
less_than_irreflexivity,
list-cases,
ml_apply-sq,
nil_wf,
list-valueall-type,
void-valueall-type,
subtype_base_sq,
int-vec-add_wf,
product_subtype_list,
spread_cons_lemma,
equal_wf,
set_subtype_base,
le_wf,
cons_wf,
int-valueall-type,
colength_wf_list,
intformeq_wf,
itermAdd_wf,
int_formula_prop_eq_lemma,
int_term_value_add_lemma,
equal-wf-T-base,
decidable__le,
intformnot_wf,
int_formula_prop_not_lemma,
subtract_wf,
itermSubtract_wf,
int_term_value_subtract_lemma,
decidable__equal_int,
null_cons_lemma
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
thin,
lambdaFormation,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
hypothesis,
setElimination,
rename,
intWeakElimination,
natural_numberEquality,
independent_isectElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
sqequalRule,
independent_pairFormation,
computeAll,
independent_functionElimination,
sqequalAxiom,
baseApply,
closedConclusion,
baseClosed,
applyEquality,
because_Cache,
unionElimination,
instantiate,
cumulativity,
equalityTransitivity,
equalitySymmetry,
promote_hyp,
hypothesis_subsumption,
productElimination,
applyLambdaEquality,
dependent_set_memberEquality,
addEquality,
imageElimination
Latex:
\mforall{}[as,bs:\mBbbZ{} List]. (ml-int-vec-add(as;bs) \msim{} as + bs)
Date html generated:
2017_09_29-PM-05_56_51
Last ObjectModification:
2017_05_19-PM-06_24_01
Theory : omega
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