A Markdown-only Structured Derivation
I am happy today. I have written a structured derivation using only markdown. Here it is:
● a ⊓ b = a ⇒ a ⊑ b
⊩ Prove ⇒
● a ⇒ b
1. a ⊓ b = a
≡ Textual substitution using 1
a ⊓ b ⇒ b
⇐ Meet elimination
true
▢
▢
● a ⊑ b ⇒ a ⊓ b = a
⊩ Prove ⇒
● a ⊓ b = a
1. a ⊑ b
⇐ ⊑ Antisymmetric
a ⊓ b ⊑ a ⋀ a ⊑ a ⊓ b
⇐ ⊓ Elimination
a ⊑ a ⊓ b
⇐ ⊓ Introduction
a ⊑ a ⋀ a ⊑ b
⇐ ⊑ Reflexive
a ⊑ b
⇐ Assumption 1.
true
▢
▢
❤️