Discovery / Formal proof construction
The logic case
Resolve linked possibilities and turn a useful intermediate fact into a complete argument.
The gatekeeper’s argument
Prove that the gate opens whatever the weather and whichever pass is presented. Build your own intermediate lemmas, then assemble the final argument. “Or” requires covering both cases.
- P1Rain or Wind
- P2Red pass or Blue pass
- P3Rain → Shelter
- P4Wind → Shelter
- P5Red pass → Permit
- P6Blue pass → Permit
- P7Shelter and Permit → Gate open
Discover a reusable lemma
Assume Rain
This assumption stays inside this branch.
Assume Wind
This assumption stays inside this branch.
Assemble the final proof
Experiment, make a prediction, and check your solution when ready.
Need a hint?
First find what is true in both weather cases. Repeat that reasoning for the two pass cases. Only established lemmas may be used in the final proof.