Nuprl Lemma : decidable__divides
∀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 :
all: ∀x:A. B[x],
member: t ∈ T,
decidable: Dec(P),
or: P ∨ Q,
prop: ℙ,
uall: ∀[x:A]. B[x],
not: ¬A,
implies: P ⇒ Q,
uimplies: b supposing a,
false: False,
nequal: a ≠ b ∈ T ,
subtype_rel: A ⊆r B,
int_nzero: ℤ-o,
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
decidable__equal_int,
istype-int,
decidable_wf,
divides_wf,
any_divs_zero,
not_wf,
zero_divs_only_zero,
decidable_functionality,
equal-wf-base,
int_subtype_base,
divides_iff_rem_zero,
nequal_wf,
decidable__int_equal
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :lambdaFormation_alt,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
natural_numberEquality,
hypothesis,
unionElimination,
Error :inhabitedIsType,
equalityTransitivity,
equalitySymmetry,
hyp_replacement,
applyLambdaEquality,
isectElimination,
Error :inlFormation_alt,
Error :universeIsType,
Error :inrFormation_alt,
independent_isectElimination,
independent_functionElimination,
voidElimination,
intEquality,
remainderEquality,
applyEquality,
sqequalRule,
Error :dependent_set_memberEquality_alt,
productElimination,
because_Cache
Latex:
\mforall{}a,b:\mBbbZ{}. Dec(a | b)
Date html generated:
2019_06_20-PM-02_20_33
Last ObjectModification:
2018_10_03-AM-00_35_46
Theory : num_thy_1
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