You cannot select more than 25 topics Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
lean4game/server/nng/NNG/Levels/AdvProposition/Level_8.lean

50 lines
672 B
Plaintext

This file contains ambiguous Unicode characters!

This file contains ambiguous Unicode characters that may be confused with others in your current locale. If your use case is intentional and legitimate, you can safely ignore this warning. Use the Escape button to highlight these characters.

import NNG.Metadata
import NNG.MyNat.Addition
import Std.Tactic.RCases
import Mathlib.Tactic.LeftRight
Game "NNG"
World "AdvProposition"
Level 8
Title ""
open MyNat
Introduction
"
"
Statement and_or_distrib_left
""
(P Q R : Prop) : P ∧ (Q R) ↔ (P ∧ Q) (P ∧ R) := by
constructor
intro h
rcases h with ⟨hp, hqr⟩
rcases hqr with q | r
left
constructor
assumption
assumption
right
constructor
assumption
assumption
intro h
rcases h with hpq | hpr
rcases hpq with ⟨p, q⟩
constructor
assumption
left
assumption
rcases hpr with ⟨hp, hr⟩
constructor
assumption
right
assumption
Conclusion
"
"