Rule of Substitution/Technical Note
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Technical Note on Rule of Substitution
When invoking the Rule of Substitution in a tableau proof, use the {{Substitution}}
template:
{{Substitution|line|pool|statement|depends|instance 1}}
{{Substitution|line|pool|statement|depends|instance 1|substitution 1}}
{{Substitution|line|pool|statement|depends|instance 1|substitution 1|instance 2|substitution 2}}
{{Substitution|line|pool|statement|depends|instance 1|substitution 1|instance 2|substitution 2|instance 3|substitution 3}}
where:
line
is the number of the line on the tableau proof where the Rule of Substitution is to be invokedpool
is the pool of assumptions (comma-separated list) of the statement on which the Rule of Substitution is to be usedstatement
is the statement of logic that is to be displayed in the Formula column, without the$ ... $
delimitersdepends
is the line of the tableau proof of the statement on which the Rule of Substitution is to be used
instance 1
is that which is being substitutedsubstitution 1
is what it is being replaced with
Optionally you can perform up to $3$ substitutions:
instance 2
is that which is being substituted: instance 2substitution 2
is what it is being replaced with: instance 2
instance 3
is that which is being substituted: instance 3substitution 3
is what it is being replaced with: instance 3.