Nuprl Lemma : gcd_com
∀[n,m:ℕ]. (gcd(n;m) ~ gcd(m;n))
Proof
Definitions occuring in Statement :
gcd: gcd(a;b),
nat: ℕ,
uall: ∀[x:A]. B[x],
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x]
Lemmas referenced :
gcd_sym_nat,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
hypothesis,
sqequalAxiom,
sqequalRule,
isect_memberEquality,
isectElimination,
because_Cache
Latex:
\mforall{}[n,m:\mBbbN{}]. (gcd(n;m) \msim{} gcd(m;n))
Date html generated:
2016_05_14-PM-09_24_27
Last ObjectModification:
2015_12_26-PM-08_03_38
Theory : num_thy_1
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