Nuprl Lemma : comb_for_gcd_wf
λa,b,z. gcd(a;b) ∈ a:ℤ ⟶ b:ℤ ⟶ (↓True) ⟶ ℤ
Proof
Definitions occuring in Statement :
gcd: gcd(a;b),
squash: ↓T,
true: True,
member: t ∈ T,
lambda: λx.A[x],
function: x:A ⟶ B[x],
int: ℤ
Definitions unfolded in proof :
member: t ∈ T,
squash: ↓T,
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
prop: ℙ
Lemmas referenced :
gcd_wf,
squash_wf,
true_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :lambdaEquality_alt,
sqequalHypSubstitution,
imageElimination,
cut,
introduction,
extract_by_obid,
dependent_functionElimination,
thin,
hypothesisEquality,
equalityTransitivity,
hypothesis,
equalitySymmetry,
Error :universeIsType,
isectElimination,
Error :inhabitedIsType,
intEquality
Latex:
\mlambda{}a,b,z. gcd(a;b) \mmember{} a:\mBbbZ{} {}\mrightarrow{} b:\mBbbZ{} {}\mrightarrow{} (\mdownarrow{}True) {}\mrightarrow{} \mBbbZ{}
Date html generated:
2019_06_20-AM-11_25_25
Last ObjectModification:
2018_09_28-AM-00_34_13
Theory : arithmetic
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