Conditional proof is a proof that takes the form of asserting a conditional, and proving that the premise or antecedent of the conditional necessarily leads to the conclusion. Proving this requires assuming the premise and deriving, from that assumption, the consequent of the conditional. By proving the connection between the antecedent and the consequent, the assumption of the antecedent is justified post hoc.

For example, I claim that "if you don't leave now, you'll be late for work". I prove it with the following argument:

It takes twenty minutes to get to work.

You're supposed to start work in twenty minutes.

Assume you don't leave now.

When you do leave, you'll arrive after the time you're supposed to start.

∴ If you don't leave now, you'll be late for work.

Note that I haven't proved that you'll be late for work: I've only proven the conditional, that the consequent follows necessarily from the antecedent.

The only difference from material conditional is the case when the hypothesis is false but the conclusion is true.

In that case, in conditional, the result is true, yet in biconditional the result is false.

When a theorem and its reciprocal are true we say that its hypothesis is the necessary and sufficient condition of the thesis; that is to say, that it is at the same time both cause and consequence.

Conditional branch instructions specify a condition to be tested for, and the address of a new instruction to be executed if a specified condition is met.

If a second conditional branch instruction is decoded, and one of the Instruction Buffers 31, 32 or 33 is not active, a third instruction fetch for a third instruction stream may be initiated, and the same determination as to the success of the conditional branch instruction made.

If the conditional branch is not of the known successful type, indicated on line 134, then the active trigger of the instruction stream containing the conditional branch instruction is left in an active state to continue instruction fetch requests as required.

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