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:
2018_05_21-PM-07_52_35
Last ObjectModification:
2018_05_19-PM-04_50_20
Theory : general
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