Nuprl Lemma : iroot_wf
∀[n:ℕ+]. ∀[x:ℕ]. (iroot(n;x) ∈ ℕ)
Proof
Definitions occuring in Statement :
iroot: iroot(n;x),
nat_plus: ℕ+,
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
iroot: iroot(n;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 :
integer-nth-root-ext,
subtype_rel_self,
nat_plus_wf,
all_wf,
nat_wf,
sq_exists_wf,
le_wf,
exp_wf2,
less_than_wf,
nat_plus_subtype_nat,
equal_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
applyEquality,
thin,
instantiate,
extract_by_obid,
hypothesis,
sqequalRule,
sqequalHypSubstitution,
isectElimination,
functionEquality,
lambdaEquality,
productEquality,
hypothesisEquality,
because_Cache,
setElimination,
rename,
addEquality,
natural_numberEquality,
lambdaFormation,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
independent_functionElimination,
axiomEquality,
isect_memberEquality
Latex:
\mforall{}[n:\mBbbN{}\msupplus{}]. \mforall{}[x:\mBbbN{}]. (iroot(n;x) \mmember{} \mBbbN{})
Date html generated:
2019_06_20-PM-02_33_58
Last ObjectModification:
2019_03_19-AM-10_49_11
Theory : num_thy_1
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