The UN General Assembly regards February 20 as the World Day of Social Justice. One way to further the cause of social justice is to fuck up Escalades.
I used Isa's banana bread recipe and mixed in 1/4 c. chocolate chips. I only baked it for an hour but might try 50 min. next time. Or just buy a proper bread pan.
Here's a sketch of a derivation of an inductive principle for S5, that if A→□B is a theorem, then ◊A→B is a theorem:
1. A→□B [hypothesis]
2. □B→B [T axiom]
3. A→B [propositional logic]
4. A→◊A [T◊ theorem]
5. ◊A→B [propositional logic]
We can then use this inductive principle — call it IP — to prove that ◊□A→□◊A is a theorem:
1. A→□◊A [B theorem]
2. □(A→□◊A) [rule of necessitation]
3. □(A→□◊A)→(□A→□□◊A) [K axiom]
4. □A→□□◊A [modus ponens]
5. ◊□A→□◊A [IP]