Nuprl Lemma : test1
∀p:ℕ × ℕ. ∀bs:ℕ List. (let x,y = p in x + y ∈ ℤ)
Proof
Definitions occuring in Statement :
list: T List,
nat: ℕ,
all: ∀x:A. B[x],
member: t ∈ T,
spread: spread def,
product: x:A × B[x],
add: n + m,
int: ℤ
Definitions unfolded in proof :
member: t ∈ T,
nat: ℕ,
uall: ∀[x:A]. B[x],
ge: i ≥ j ,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
implies: P ⇒ Q,
not: ¬A,
top: Top,
and: P ∧ Q,
prop: ℙ,
subtype_rel: A ⊆r B,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2]
Lemmas referenced :
spread_wf,
list_wf,
le_wf,
int_formula_prop_wf,
int_term_value_var_lemma,
int_term_value_add_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_not_lemma,
int_formula_prop_and_lemma,
itermVar_wf,
itermAdd_wf,
itermConstant_wf,
intformle_wf,
intformnot_wf,
intformand_wf,
satisfiable-full-omega-tt,
decidable__le,
nat_properties,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
cut,
lemma_by_obid,
hypothesis,
dependent_set_memberEquality,
addEquality,
sqequalHypSubstitution,
setElimination,
thin,
rename,
hypothesisEquality,
isectElimination,
dependent_functionElimination,
natural_numberEquality,
unionElimination,
independent_isectElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
sqequalRule,
independent_pairFormation,
computeAll,
because_Cache,
productEquality,
lambdaFormation,
applyEquality
Latex:
\mforall{}p:\mBbbN{} \mtimes{} \mBbbN{}. \mforall{}bs:\mBbbN{} List. (let x,y = p in x + y \mmember{} \mBbbZ{})
Date html generated:
2016_05_15-PM-07_46_04
Last ObjectModification:
2016_01_16-AM-09_34_02
Theory : general
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