Nuprl Lemma : isqrt_wf
∀[x:ℕ]. (isqrt(x) ∈ ℕ)
Proof
Definitions occuring in Statement :
isqrt: isqrt(x)
,
nat: ℕ
,
uall: ∀[x:A]. B[x]
,
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x]
,
member: t ∈ T
,
isqrt: isqrt(x)
,
subtype_rel: A ⊆r B
,
all: ∀x:A. B[x]
,
so_lambda: λ2x.t[x]
,
prop: ℙ
,
and: P ∧ Q
,
nat: ℕ
,
so_apply: x[s]
,
sq_exists: ∃x:A [B[x]]
,
implies: P
⇒ Q
Lemmas referenced :
nat_wf,
integer-sqrt-ext,
subtype_rel_self,
sq_exists_wf,
le_wf,
less_than_wf,
equal_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
sqequalHypSubstitution,
axiomEquality,
equalityTransitivity,
hypothesis,
equalitySymmetry,
extract_by_obid,
applyEquality,
thin,
instantiate,
isectElimination,
functionEquality,
lambdaEquality,
productEquality,
multiplyEquality,
setElimination,
rename,
hypothesisEquality,
because_Cache,
addEquality,
natural_numberEquality,
lambdaFormation,
dependent_functionElimination,
independent_functionElimination
Latex:
\mforall{}[x:\mBbbN{}]. (isqrt(x) \mmember{} \mBbbN{})
Date html generated:
2019_06_20-PM-02_36_45
Last ObjectModification:
2019_06_12-PM-00_25_43
Theory : num_thy_1
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