Nuprl Lemma : tsqrt_wf
∀[n:ℕ]. (tsqrt(n) ∈ ℕ)
Proof
Definitions occuring in Statement :
tsqrt: tsqrt(n),
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
tsqrt: tsqrt(n),
nat: ℕ,
ge: i ≥ j ,
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],
false: False,
top: Top,
and: P ∧ Q,
prop: ℙ,
has-value: (a)↓,
so_lambda: λ2x.t[x],
so_apply: x[s],
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
subtype_rel: A ⊆r B,
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
bfalse: ff,
guard: {T},
sq_type: SQType(T)
Lemmas referenced :
isqrt_wf,
nat_properties,
decidable__le,
full-omega-unsat,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermMultiply_wf,
itermVar_wf,
istype-int,
int_formula_prop_and_lemma,
istype-void,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_mul_lemma,
int_term_value_var_lemma,
int_formula_prop_wf,
istype-le,
istype-nat,
value-type-has-value,
nat_wf,
set-value-type,
le_wf,
int-value-type,
le_int_wf,
uiff_transitivity,
equal-wf-base,
bool_wf,
set_subtype_base,
int_subtype_base,
assert_wf,
eqtt_to_assert,
assert_of_le_int,
lt_int_wf,
less_than_wf,
bnot_wf,
eqff_to_assert,
assert_functionality_wrt_uiff,
bnot_of_le_int,
assert_of_lt_int,
decidable__equal_int,
subtype_base_sq,
intformless_wf,
itermAdd_wf,
int_formula_prop_less_lemma,
int_term_value_add_lemma,
subtract_wf,
itermSubtract_wf,
intformeq_wf,
int_term_value_subtract_lemma,
int_formula_prop_eq_lemma
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
dependent_set_memberEquality_alt,
multiplyEquality,
natural_numberEquality,
setElimination,
rename,
hypothesisEquality,
hypothesis,
dependent_functionElimination,
unionElimination,
independent_isectElimination,
approximateComputation,
independent_functionElimination,
dependent_pairFormation_alt,
lambdaEquality_alt,
int_eqEquality,
isect_memberEquality_alt,
voidElimination,
sqequalRule,
independent_pairFormation,
universeIsType,
inhabitedIsType,
lambdaFormation_alt,
equalityIstype,
equalityTransitivity,
equalitySymmetry,
axiomEquality,
callbyvalueReduce,
intEquality,
addEquality,
because_Cache,
equalityElimination,
baseApply,
closedConclusion,
baseClosed,
applyEquality,
productElimination,
instantiate,
cumulativity,
applyLambdaEquality
Latex:
\mforall{}[n:\mBbbN{}]. (tsqrt(n) \mmember{} \mBbbN{})
Date html generated:
2020_05_19-PM-10_03_48
Last ObjectModification:
2019_11_22-AM-10_51_19
Theory : num_thy_1
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