Rule of Substitution/Technical Note

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 invoked

pool is the pool of assumptions (comma-separated list) of the statement on which the Rule of Substitution is to be used

statement is the statement of logic that is to be displayed in the Formula column, without the $ ... $ delimiters

depends 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 substituted

substitution 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 2

substitution 2 is what it is being replaced with: instance 2

instance 3 is that which is being substituted: instance 3

substitution 3 is what it is being replaced with: instance 3.