Nuprl Lemma : gcd_reduce_wf
∀[p,q:ℤ]. (gcd_reduce(p;q) ∈ ℕ × ℤ × ℤ)
Proof
Definitions occuring in Statement :
gcd_reduce: gcd_reduce(p;q),
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
product: x:A × B[x],
int: ℤ
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
gcd_reduce: gcd_reduce(p;q),
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],
exists: ∃x:A. B[x],
implies: P ⇒ Q,
spreadn: spread4
Lemmas referenced :
gcd-reduce-ext,
subtype_rel_self,
all_wf,
exists_wf,
nat_wf,
equal-wf-base-T,
int_subtype_base,
equal-wf-base,
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,
intEquality,
lambdaEquality,
productEquality,
hypothesisEquality,
multiplyEquality,
setElimination,
rename,
because_Cache,
baseApply,
closedConclusion,
baseClosed,
lambdaFormation,
spreadEquality,
productElimination,
dependent_pairEquality,
independent_pairEquality,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
independent_functionElimination,
axiomEquality,
isect_memberEquality
Latex:
\mforall{}[p,q:\mBbbZ{}]. (gcd\_reduce(p;q) \mmember{} \mBbbN{} \mtimes{} \mBbbZ{} \mtimes{} \mBbbZ{})
Date html generated:
2018_05_21-PM-00_59_30
Last ObjectModification:
2018_05_19-AM-06_35_44
Theory : num_thy_1
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