Proof. At the investigation, did the `judge' obtain substantial evidence or proof that the employee was guilty as charged?"
Proof. The cardholder agrees and accepts that his monthly account statement constitutes conclusive proof of indebtedness and agrees to pay the indebtedness shown on his monthly account statement in accordance with the terms of this Agreement. The cardholder agrees to review each monthly statement and if an error is found, the cardholder must tell Desjardins within 30 days of the issue date of the statement. If the cardholder does not do so, the statement will be regarded as final. However, Desjardins may at any time remove from the cardholder’s account any credits that have been posted in error. The cardholder also agrees and accepts that the transaction record issued by an accessible device constitutes proof that the transaction he has carried out has been correctly recorded. In the case of a card-not-present or contactless transaction, as indicated under Section 22 of this Agreement, the cardholder agrees that the entry of the transaction on his monthly account statement will constitute proof that the transaction was carried out. Desjardins is not responsible for providing other proof of transactions, unless the cardholder requests it to avoid or settle a dispute within the meaning of this Agreement, unless in such case, he provides Desjardins with a transaction record confirming the purchase or the cash advance. The cardholder agrees that any data support on which the data pertaining to the transactions made is stored constitutes a sufficient written proof for all legal proceedings.
Proof. A doctor’s certificate or other adequate proof shall be provided by the employee in all cases of absence due to illness when requested by the appointing authority.
Proof. All sick leave used shall be certified by the employee and by such other evidence as the Employer may require. Falsification of such evidence may be cause for disciplinary action up to and including dismissal. The Employer may require that an employee present medical certification of physical or mental fitness to continue working.
Proof. All requests for use of sick leave shall be certified by the unit employee as to its purpose. The Appointing Authority may require that a unit employee, at the Appointing Authority's cost, present medical certification of physical or mental fitness to continue working.
Proof. Proof of death, attendance at the funeral or travel distance may be required by the EMPLOYER.
Proof. By assumption H, at least two values v and u are written in T [R + K]. It follows from Lemma 1 that v and u must have been written in T [R + i] for each i such that 1 ≤ i < K. It remains to show that such a write operation with parameter v (resp. u) occurs in ei. Let us consider the first write of v in T [R + i]. Clearly, this operation occurs in epoch eR+i′ , for some i′ ≥ i. Suppose for the sake of contradiction that i′ > i. Hence, the first time v is written in T [R + i], a value has already been written in T [R + i + 1]. Let p be the process that performs this first write of v in T [R + i + 1]. As v is written to T [R + K], p must exist by Lemma 1. Denote wp(R +i+1) the write operation of p. According to the code of Janus we know that: (1) p performs that operation while it is executing round R + i + 1 (line 7), (2) wp(R + i + 1) is preceded by a read operation of T [R + i + 1] (denoted rp(R + i + 1)) by p that returns ⊥ , and (3) in round R + i, there is a read operation from T [R + i] that returns v or a write of v by p to T [R + i]. Denote by opp(R + i) this last operation, and opp(R + i), rp(R + i + 1), wp(R + i + 1) the operations that occur in this order. Moreover, opp(R + i), which reads or writes v in T [R + i] occurs in epoch eR+i′′ for some i′′ ≥ i′, since the write of v in T [R + i] occurs in eR+i′ . Therefore, operation rp(R + i + 1) occurs after a write in T [R + i + 1], from which we conclude that rp(R + i + 1) returns a non-⊥ value. It thus follows by Xxxxx 4 that p does not write in T [R + i + 1] : a contradiction. We have shown that a write of v in T [R + i] occurs in epoch ei. A similar argument applied to value u yields that a write of u in T [R + i] occurs in ei. Since each process does not write twice in the same register, |Wi| ≥ 2.
Proof. If the height of α is 0, and the common frontier (α itself) exists, then α is common. If the height of α is σ, the children of α are all in common by using induction hypothesis with the height of the children at σ-1, then the vertex α is common. ■
Proof. With f = 1 and n 4 we have at least 3 correct nodes. A correct node will see every correct value at least twice, once directly from another correct node, and once through the third correct node. So all correct values are in T . If the byzantine node sends the same value to at least 2 other (correct) nodes, all correct nodes will see the value twice, so all add it to set T . If the byzantine node sends all different values to the correct nodes, none of these values will end up in any set T .
