Nuprl Lemma : gcd_assoc_nat
∀a,b,c:ℕ. (gcd(gcd(a;b);c) ~ gcd(a;gcd(b;c)))
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_assoc,
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,
because_Cache,
independent_isectElimination,
hypothesis,
dependent_functionElimination,
setElimination,
rename,
hypothesisEquality,
dependent_set_memberEquality,
natural_numberEquality,
productElimination,
independent_functionElimination,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}a,b,c:\mBbbN{}. (gcd(gcd(a;b);c) \msim{} gcd(a;gcd(b;c)))
Date html generated:
2016_05_14-PM-09_23_57
Last ObjectModification:
2015_12_26-PM-08_04_25
Theory : num_thy_1
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