Nuprl Lemma : decidable__divides_ext
∀a,b:ℤ. Dec(a | b)
Proof
Definitions occuring in Statement :
divides: b | a,
decidable: Dec(P),
all: ∀x:A. B[x],
int: ℤ
Definitions unfolded in proof :
member: t ∈ T,
divide: n ÷ m,
pi1: fst(t),
decidable__divides,
decidable__equal_int,
any_divs_zero,
any: any x,
decidable_functionality,
divides_iff_rem_zero,
decidable__int_equal,
iff_preserves_decidability,
uall: ∀[x:A]. B[x],
so_lambda: so_lambda(x,y,z,w.t[x; y; z; w]),
so_apply: x[s1;s2;s3;s4],
so_lambda: λ2x.t[x],
top: Top,
so_apply: x[s],
uimplies: b supposing a
Lemmas referenced :
decidable__divides,
lifting-strict-int_eq,
istype-void,
strict4-decide,
decidable__equal_int,
any_divs_zero,
decidable_functionality,
divides_iff_rem_zero,
decidable__int_equal,
iff_preserves_decidability
Rules used in proof :
introduction,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
cut,
instantiate,
extract_by_obid,
hypothesis,
sqequalRule,
thin,
sqequalHypSubstitution,
equalityTransitivity,
equalitySymmetry,
isectElimination,
baseClosed,
Error :isect_memberEquality_alt,
voidElimination,
independent_isectElimination
Latex:
\mforall{}a,b:\mBbbZ{}. Dec(a | b)
Date html generated:
2019_06_20-PM-02_20_35
Last ObjectModification:
2019_03_10-PM-11_03_43
Theory : num_thy_1
Home
Index