Nuprl Lemma : gcd_sym_nat
∀a,b:ℕ.  (gcd(a;b) ~ gcd(b;a))
Proof
Definitions occuring in Statement : 
gcd: gcd(a;b)
, 
nat: ℕ
, 
all: ∀x:A. B[x]
, 
sqequal: s ~ t
Definitions unfolded in proof : 
all: ∀x:A. B[x]
, 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
uimplies: b supposing a
, 
nat: ℕ
, 
prop: ℙ
, 
iff: P 
⇐⇒ Q
, 
and: P ∧ Q
, 
implies: P 
⇒ Q
, 
sq_type: SQType(T)
, 
guard: {T}
Lemmas referenced : 
subtype_base_sq, 
int_subtype_base, 
gcd_sym, 
assoced_nelim, 
gcd_wf, 
gcd-non-neg, 
le_wf, 
nat_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
lambdaFormation, 
cut, 
thin, 
instantiate, 
lemma_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
cumulativity, 
intEquality, 
independent_isectElimination, 
hypothesis, 
dependent_functionElimination, 
setElimination, 
rename, 
hypothesisEquality, 
dependent_set_memberEquality, 
natural_numberEquality, 
because_Cache, 
productElimination, 
independent_functionElimination, 
equalityTransitivity, 
equalitySymmetry
Latex:
\mforall{}a,b:\mBbbN{}.    (gcd(a;b)  \msim{}  gcd(b;a))
Date html generated:
2016_05_14-PM-09_23_54
Last ObjectModification:
2015_12_26-PM-08_04_22
Theory : num_thy_1
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