Nuprl Lemma : exp2
∀[i:ℤ]. (i^2 = (i * i) ∈ ℤ)
Proof
Definitions occuring in Statement :
exp: i^n,
uall: ∀[x:A]. B[x],
multiply: n * m,
natural_number: $n,
int: ℤ,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
nat_plus: ℕ+,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
not: ¬A,
implies: P ⇒ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
top: Top,
prop: ℙ,
false: False,
subtract: n - m,
squash: ↓T,
true: True,
subtype_rel: A ⊆r B,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
exp_step,
decidable__lt,
full-omega-unsat,
intformnot_wf,
intformless_wf,
itermConstant_wf,
istype-int,
int_formula_prop_not_lemma,
istype-void,
int_formula_prop_less_lemma,
int_term_value_constant_lemma,
int_formula_prop_wf,
istype-less_than,
equal_wf,
squash_wf,
true_wf,
istype-universe,
exp1,
subtype_rel_self,
iff_weakening_equal
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
cut,
sqequalRule,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
Error :dependent_set_memberEquality_alt,
natural_numberEquality,
dependent_functionElimination,
hypothesis,
unionElimination,
independent_isectElimination,
approximateComputation,
independent_functionElimination,
Error :dependent_pairFormation_alt,
Error :lambdaEquality_alt,
Error :isect_memberEquality_alt,
voidElimination,
Error :universeIsType,
hypothesisEquality,
applyEquality,
imageElimination,
equalityTransitivity,
equalitySymmetry,
Error :inhabitedIsType,
instantiate,
universeEquality,
intEquality,
multiplyEquality,
because_Cache,
imageMemberEquality,
baseClosed,
productElimination
Latex:
\mforall{}[i:\mBbbZ{}]. (i\^{}2 = (i * i))
Date html generated:
2019_06_20-PM-01_18_44
Last ObjectModification:
2019_02_01-PM-01_25_13
Theory : int_2
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