Nuprl Lemma : divides_transitivity
∀a,b,c:ℤ. ((a | b) ⇒ (b | c) ⇒ (a | c))
Proof
Definitions occuring in Statement :
divides: b | a,
all: ∀x:A. B[x],
implies: P ⇒ Q,
int: ℤ
Definitions unfolded in proof :
divides: b | a,
all: ∀x:A. B[x],
implies: P ⇒ Q,
exists: ∃x:A. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
prop: ℙ,
uall: ∀[x:A]. B[x],
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
not: ¬A,
satisfiable_int_formula: satisfiable_int_formula(fmla),
false: False,
top: Top,
and: P ∧ Q
Lemmas referenced :
int_subtype_base,
istype-int,
equal-wf-base,
decidable__equal_int,
full-omega-unsat,
intformand_wf,
intformnot_wf,
intformeq_wf,
itermVar_wf,
itermMultiply_wf,
int_formula_prop_and_lemma,
istype-void,
int_formula_prop_not_lemma,
int_formula_prop_eq_lemma,
int_term_value_var_lemma,
int_term_value_mul_lemma,
int_formula_prop_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
Error :lambdaFormation_alt,
Error :productIsType,
Error :inhabitedIsType,
hypothesisEquality,
Error :equalityIsType4,
cut,
applyEquality,
introduction,
extract_by_obid,
hypothesis,
sqequalHypSubstitution,
multiplyEquality,
productElimination,
thin,
Error :dependent_pairFormation_alt,
equalitySymmetry,
hyp_replacement,
applyLambdaEquality,
isectElimination,
intEquality,
dependent_functionElimination,
because_Cache,
unionElimination,
natural_numberEquality,
independent_isectElimination,
approximateComputation,
independent_functionElimination,
Error :lambdaEquality_alt,
int_eqEquality,
Error :isect_memberEquality_alt,
voidElimination,
independent_pairFormation,
Error :universeIsType
Latex:
\mforall{}a,b,c:\mBbbZ{}. ((a | b) {}\mRightarrow{} (b | c) {}\mRightarrow{} (a | c))
Date html generated:
2019_06_20-PM-02_20_06
Last ObjectModification:
2018_10_03-AM-00_35_41
Theory : num_thy_1
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