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A proof that (Theta vdash { C,mathttBoolmathtt mathttBoolmathtt) holds can be given from the entailment rules given in Fig. 7, since this is the conclusion of rule ((mathtt {MP} )) with premises (Theta vdash { D,Bool, mathttBoolmathtt) and (Theta vdash { D,Bool mathttBoolmathtt Rightarrow C,mathttBoolmathtt,mathttBoolmathtt,) and these two premises can be derived by using rule ((mathtt {INST} )).
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As is standard in proof theory, the way to read these rules of inference is that above the horizontal rule — are the the premises of the rule (which are equations) and the equation below the horizontal rule is the conclusion of the rule of inference.
Experts define the conclusions of rules as so-called half-marks in order to increase the method's flexibility.
A premise of a rule may be satisfied by the conclusion of another rule.
The conclusion of a rule appears to the left of the implication operator ":-".
Axiom sequents in LK are valid, and the conclusion of a rule is valid iff its premises are.
The conclusion of the rule is about the partial correctness of the program α1;α2 (i.e., α1 sequentially composed with α2), that follows from the two assumptions.
The implication operator is used to connect the conditions and conclusion of a rule, where the conditions appear to the right of the operator and the conclusion appear to the left of the operator.
If a 'true-branch' leads to a terminal node t, and the condition of t is not fulfilled then the conclusion of the rule in the parent node of t is taken.
When DC became the murder capital of the nation and one of the major loci of the crack epidemic, it was thought to be the logical conclusion of black rule.
It is also possible to assign a description to the conclusion of a rule.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com