Nuprl Lemma : thm_1a
∀n:ℕ. (↑isEven((n * n) + n))
Proof
Definitions occuring in Statement :
isEven: isEven(n),
nat: ℕ,
assert: ↑b,
all: ∀x:A. B[x],
multiply: n * m,
add: n + m
Definitions unfolded in proof :
true: True,
squash: ↓T,
so_apply: x[s],
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
uiff: uiff(P;Q),
guard: {T},
sq_type: SQType(T),
prop: ℙ,
top: Top,
false: False,
exists: ∃x:A. B[x],
satisfiable_int_formula: satisfiable_int_formula(fmla),
not: ¬A,
or: P ∨ Q,
decidable: Dec(P),
ge: i ≥ j ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
rev_implies: P ⇐ Q,
and: P ∧ Q,
iff: P ⇐⇒ Q,
nat: ℕ,
member: t ∈ T,
all: ∀x:A. B[x]
Lemmas referenced :
mul_assoc,
iff_weakening_equal,
subtype_rel_self,
istype-universe,
true_wf,
squash_wf,
equal_wf,
le_wf,
set_subtype_base,
assert-isOdd,
isEven_wf,
isOdd_wf,
assert_of_bor,
odd-or-even,
int_formula_prop_wf,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_term_value_mul_lemma,
int_term_value_add_lemma,
int_formula_prop_eq_lemma,
istype-void,
int_formula_prop_not_lemma,
istype-int,
itermConstant_wf,
itermVar_wf,
itermMultiply_wf,
itermAdd_wf,
intformeq_wf,
intformnot_wf,
full-omega-unsat,
decidable__equal_int,
nat_properties,
int_subtype_base,
subtype_base_sq,
assert-isEven,
istype-nat
Rules used in proof :
imageMemberEquality,
universeEquality,
imageElimination,
sqequalBase,
applyEquality,
baseClosed,
closedConclusion,
baseApply,
Error :inhabitedIsType,
Error :equalityIstype,
equalitySymmetry,
equalityTransitivity,
Error :universeIsType,
sqequalRule,
voidElimination,
Error :isect_memberEquality_alt,
int_eqEquality,
Error :lambdaEquality_alt,
Error :dependent_pairFormation_alt,
approximateComputation,
natural_numberEquality,
unionElimination,
independent_isectElimination,
intEquality,
cumulativity,
isectElimination,
instantiate,
independent_functionElimination,
productElimination,
because_Cache,
hypothesisEquality,
rename,
setElimination,
multiplyEquality,
addEquality,
thin,
dependent_functionElimination,
sqequalHypSubstitution,
hypothesis,
extract_by_obid,
introduction,
cut,
Error :lambdaFormation_alt,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}n:\mBbbN{}. (\muparrow{}isEven((n * n) + n))
Date html generated:
2019_06_20-PM-02_32_12
Last ObjectModification:
2019_06_19-PM-02_28_05
Theory : num_thy_1
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