Nuprl Lemma : gcd_sym
∀a,b:ℤ. (gcd(a;b) ~ gcd(b;a))
Proof
Definitions occuring in Statement :
assoced: a ~ b,
gcd: gcd(a;b),
all: ∀x:A. B[x],
int: ℤ
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
exists: ∃x:A. B[x],
and: P ∧ Q,
implies: P ⇒ Q,
guard: {T},
uimplies: b supposing a
Lemmas referenced :
istype-int,
gcd_elim,
gcd_p_sym,
gcd_unique,
gcd_wf,
assoced_transitivity,
assoced_weakening
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :lambdaFormation_alt,
Error :inhabitedIsType,
hypothesisEquality,
cut,
introduction,
extract_by_obid,
hypothesis,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
because_Cache,
productElimination,
independent_functionElimination,
equalityTransitivity,
equalitySymmetry,
independent_isectElimination
Latex:
\mforall{}a,b:\mBbbZ{}. (gcd(a;b) \msim{} gcd(b;a))
Date html generated:
2019_06_20-PM-02_21_59
Last ObjectModification:
2018_10_03-AM-00_12_18
Theory : num_thy_1
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