is_true
bool 2
classes | length
int64 0
225
| prompt
stringlengths 65
106
| completion
stringlengths 11
17.1k
|
|---|---|---|---|
true
| 2
|
<state id="0"><if>p1 p2 p3 : Prop</if><then>⊢ True ∨ (True → True)</then></state>||
|
<tactic>apply Or.inl</tactic><state id="1"><if>case h</if><if>p1 p2 p3 : Prop</if><then>⊢ True</then></state><tactic>apply True.intro</tactic><state id="2"><complete /></state><success />
|
true
| 2
|
<state id="0"><if>p1 p2 p3 : Prop</if><then>⊢ True ∨ True ∧ False</then></state>||
|
<tactic>apply Or.inl</tactic><state id="1"><if>case h</if><if>p1 p2 p3 : Prop</if><then>⊢ True</then></state><tactic>apply True.intro</tactic><state id="2"><complete /></state><success />
|
true
| 2
|
<state id="0"><if>p1 p2 p3 : Prop</if><then>⊢ True ∨ (False → False)</then></state>||
|
<tactic>apply Or.inl</tactic><state id="1"><if>case h</if><if>p1 p2 p3 : Prop</if><then>⊢ True</then></state><tactic>apply True.intro</tactic><state id="2"><complete /></state><success />
|
true
| 2
|
<state id="0"><if>p1 p2 p3 : Prop</if><then>⊢ True ∨ True ∧ p3</then></state>||
|
<tactic>apply Or.inl</tactic><state id="1"><if>case h</if><if>p1 p2 p3 : Prop</if><then>⊢ True</then></state><tactic>apply True.intro</tactic><state id="2"><complete /></state><success />
|
true
| 2
|
<state id="0"><if>p1 p2 p3 : Prop</if><then>⊢ True ∨ p1 ∧ True</then></state>||
|
<tactic>apply Or.inl</tactic><state id="1"><if>case h</if><if>p1 p2 p3 : Prop</if><then>⊢ True</then></state><tactic>apply True.intro</tactic><state id="2"><complete /></state><success />
|
true
| 2
|
<state id="0"><if>p1 p2 p3 : Prop</if><then>⊢ True ∨ (p1 → False)</then></state>||
|
<tactic>apply Or.inl</tactic><state id="1"><if>case h</if><if>p1 p2 p3 : Prop</if><then>⊢ True</then></state><tactic>apply True.intro</tactic><state id="2"><complete /></state><success />
|
true
| 2
|
<state id="0"><if>p1 p2 p3 : Prop</if><then>⊢ True ∨ (p3 → p1)</then></state>||
|
<tactic>apply Or.inl</tactic><state id="1"><if>case h</if><if>p1 p2 p3 : Prop</if><then>⊢ True</then></state><tactic>apply True.intro</tactic><state id="2"><complete /></state><success />
|
true
| 2
|
<state id="0"><if>p1 p2 p3 : Prop</if><then>⊢ True ∨ (False → p1)</then></state>||
|
<tactic>apply Or.inl</tactic><state id="1"><if>case h</if><if>p1 p2 p3 : Prop</if><then>⊢ True</then></state><tactic>apply True.intro</tactic><state id="2"><complete /></state><success />
|
true
| 2
|
<state id="0"><if>p1 p2 p3 : Prop</if><then>⊢ True ∨ p3</then></state>||
|
<tactic>apply Or.inl</tactic><state id="1"><if>case h</if><if>p1 p2 p3 : Prop</if><then>⊢ True</then></state><tactic>apply True.intro</tactic><state id="2"><complete /></state><success />
|
true
| 2
|
<state id="0"><if>p1 p2 p3 : Prop</if><then>⊢ True ∨ False ∧ p2</then></state>||
|
<tactic>apply Or.inl</tactic><state id="1"><if>case h</if><if>p1 p2 p3 : Prop</if><then>⊢ True</then></state><tactic>apply True.intro</tactic><state id="2"><complete /></state><success />
|
true
| 2
|
<state id="0"><if>p1 p2 p3 : Prop</if><then>⊢ True ∨ (p3 → False)</then></state>||
|
<tactic>apply Or.inl</tactic><state id="1"><if>case h</if><if>p1 p2 p3 : Prop</if><then>⊢ True</then></state><tactic>apply True.intro</tactic><state id="2"><complete /></state><success />
|
true
| 2
|
<state id="0"><if>p1 p2 p3 : Prop</if><then>⊢ True ∨ (p2 → p2)</then></state>||
|
<tactic>apply Or.inl</tactic><state id="1"><if>case h</if><if>p1 p2 p3 : Prop</if><then>⊢ True</then></state><tactic>apply True.intro</tactic><state id="2"><complete /></state><success />
|
true
| 2
|
<state id="0"><if>p1 p2 p3 : Prop</if><then>⊢ True ∨ p1 ∧ p2</then></state>||
|
<tactic>apply Or.inl</tactic><state id="1"><if>case h</if><if>p1 p2 p3 : Prop</if><then>⊢ True</then></state><tactic>apply True.intro</tactic><state id="2"><complete /></state><success />
|
true
| 2
|
<state id="0"><if>p1 p2 p3 : Prop</if><then>⊢ True ∨ p2 ∧ False</then></state>||
|
<tactic>apply Or.inl</tactic><state id="1"><if>case h</if><if>p1 p2 p3 : Prop</if><then>⊢ True</then></state><tactic>apply True.intro</tactic><state id="2"><complete /></state><success />
|
true
| 2
|
<state id="0"><if>p1 p2 p3 : Prop</if><then>⊢ True ∨ p2 ∧ p1</then></state>||
|
<tactic>apply Or.inl</tactic><state id="1"><if>case h</if><if>p1 p2 p3 : Prop</if><then>⊢ True</then></state><tactic>apply True.intro</tactic><state id="2"><complete /></state><success />
|
true
| 2
|
<state id="0"><if>p1 p2 p3 : Prop</if><then>⊢ True ∨ p3 ∧ True</then></state>||
|
<tactic>apply Or.inl</tactic><state id="1"><if>case h</if><if>p1 p2 p3 : Prop</if><then>⊢ True</then></state><tactic>apply True.intro</tactic><state id="2"><complete /></state><success />
|
true
| 2
|
<state id="0"><if>p1 p2 p3 : Prop</if><then>⊢ True ∨ (p3 → p3)</then></state>||
|
<tactic>apply Or.inl</tactic><state id="1"><if>case h</if><if>p1 p2 p3 : Prop</if><then>⊢ True</then></state><tactic>apply True.intro</tactic><state id="2"><complete /></state><success />
|
true
| 2
|
<state id="0"><if>p1 p2 p3 : Prop</if><then>⊢ True ∨ True ∧ p1</then></state>||
|
<tactic>apply Or.inl</tactic><state id="1"><if>case h</if><if>p1 p2 p3 : Prop</if><then>⊢ True</then></state><tactic>apply True.intro</tactic><state id="2"><complete /></state><success />
|
true
| 2
|
<state id="0"><if>p1 p2 p3 : Prop</if><then>⊢ True ∨ (False → p3)</then></state>||
|
<tactic>apply Or.inl</tactic><state id="1"><if>case h</if><if>p1 p2 p3 : Prop</if><then>⊢ True</then></state><tactic>apply True.intro</tactic><state id="2"><complete /></state><success />
|
true
| 2
|
<state id="0"><if>p1 p2 p3 : Prop</if><then>⊢ True ∨ (True → p2)</then></state>||
|
<tactic>apply Or.inl</tactic><state id="1"><if>case h</if><if>p1 p2 p3 : Prop</if><then>⊢ True</then></state><tactic>apply True.intro</tactic><state id="2"><complete /></state><success />
|
true
| 2
|
<state id="0"><if>p1 p2 p3 : Prop</if><then>⊢ True ∨ p3 ∧ p2</then></state>||
|
<tactic>apply Or.inl</tactic><state id="1"><if>case h</if><if>p1 p2 p3 : Prop</if><then>⊢ True</then></state><tactic>apply True.intro</tactic><state id="2"><complete /></state><success />
|
true
| 2
|
<state id="0"><if>p1 p2 p3 : Prop</if><then>⊢ True ∨ p2 ∧ p3</then></state>||
|
<tactic>apply Or.inl</tactic><state id="1"><if>case h</if><if>p1 p2 p3 : Prop</if><then>⊢ True</then></state><tactic>apply True.intro</tactic><state id="2"><complete /></state><success />
|
true
| 2
|
<state id="0"><if>p1 p2 p3 : Prop</if><then>⊢ True ∨ False</then></state>||
|
<tactic>apply Or.inl</tactic><state id="1"><if>case h</if><if>p1 p2 p3 : Prop</if><then>⊢ True</then></state><tactic>apply True.intro</tactic><state id="2"><complete /></state><success />
|
true
| 2
|
<state id="0"><if>p1 p2 p3 : Prop</if><then>⊢ True ∨ False ∧ True</then></state>||
|
<tactic>apply Or.inl</tactic><state id="1"><if>case h</if><if>p1 p2 p3 : Prop</if><then>⊢ True</then></state><tactic>apply True.intro</tactic><state id="2"><complete /></state><success />
|
true
| 2
|
<state id="0"><if>p1 p2 p3 : Prop</if><then>⊢ True ∨ (p2 → True)</then></state>||
|
<tactic>apply Or.inl</tactic><state id="1"><if>case h</if><if>p1 p2 p3 : Prop</if><then>⊢ True</then></state><tactic>apply True.intro</tactic><state id="2"><complete /></state><success />
|
true
| 2
|
<state id="0"><if>p1 p2 p3 : Prop</if><then>⊢ True ∨ (p1 → p3)</then></state>||
|
<tactic>apply Or.inl</tactic><state id="1"><if>case h</if><if>p1 p2 p3 : Prop</if><then>⊢ True</then></state><tactic>apply True.intro</tactic><state id="2"><complete /></state><success />
|
true
| 2
|
<state id="0"><if>p1 p2 p3 : Prop</if><then>⊢ True ∨ (p1 → p1)</then></state>||
|
<tactic>apply Or.inl</tactic><state id="1"><if>case h</if><if>p1 p2 p3 : Prop</if><then>⊢ True</then></state><tactic>apply True.intro</tactic><state id="2"><complete /></state><success />
|
true
| 2
|
<state id="0"><if>p1 p2 p3 : Prop</if><then>⊢ True ∨ False ∨ False ∧ False</then></state>||
|
<tactic>apply Or.inl</tactic><state id="1"><if>case h</if><if>p1 p2 p3 : Prop</if><then>⊢ True</then></state><tactic>apply True.intro</tactic><state id="2"><complete /></state><success />
|
true
| 2
|
<state id="0"><if>p1 p2 p3 : Prop</if><then>⊢ True ∨ (False → False ∨ False)</then></state>||
|
<tactic>apply Or.inl</tactic><state id="1"><if>case h</if><if>p1 p2 p3 : Prop</if><then>⊢ True</then></state><tactic>apply True.intro</tactic><state id="2"><complete /></state><success />
|
true
| 2
|
<state id="0"><if>p1 p2 p3 : Prop</if><then>⊢ True ∨ (False ∧ False) ∧ False</then></state>||
|
<tactic>apply Or.inl</tactic><state id="1"><if>case h</if><if>p1 p2 p3 : Prop</if><then>⊢ True</then></state><tactic>apply True.intro</tactic><state id="2"><complete /></state><success />
|
true
| 2
|
<state id="0"><if>p1 p2 p3 : Prop</if><then>⊢ True ∨ ((False → False) → False)</then></state>||
|
<tactic>apply Or.inl</tactic><state id="1"><if>case h</if><if>p1 p2 p3 : Prop</if><then>⊢ True</then></state><tactic>apply True.intro</tactic><state id="2"><complete /></state><success />
|
true
| 2
|
<state id="0"><if>p1 p2 p3 : Prop</if><then>⊢ True ∨ (False ∨ False) ∨ False</then></state>||
|
<tactic>apply Or.inl</tactic><state id="1"><if>case h</if><if>p1 p2 p3 : Prop</if><then>⊢ True</then></state><tactic>apply True.intro</tactic><state id="2"><complete /></state><success />
|
true
| 2
|
<state id="0"><if>p1 p2 p3 : Prop</if><then>⊢ True ∨ False ∨ False ∨ True</then></state>||
|
<tactic>apply Or.inl</tactic><state id="1"><if>case h</if><if>p1 p2 p3 : Prop</if><then>⊢ True</then></state><tactic>apply True.intro</tactic><state id="2"><complete /></state><success />
|
true
| 2
|
<state id="0"><if>p1 p2 p3 : Prop</if><then>⊢ True ∨ False ∧ False ∧ True</then></state>||
|
<tactic>apply Or.inl</tactic><state id="1"><if>case h</if><if>p1 p2 p3 : Prop</if><then>⊢ True</then></state><tactic>apply True.intro</tactic><state id="2"><complete /></state><success />
|
true
| 2
|
<state id="0"><if>p1 p2 p3 : Prop</if><then>⊢ True ∨ (False ∨ False) ∧ True</then></state>||
|
<tactic>apply Or.inl</tactic><state id="1"><if>case h</if><if>p1 p2 p3 : Prop</if><then>⊢ True</then></state><tactic>apply True.intro</tactic><state id="2"><complete /></state><success />
|
true
| 2
|
<state id="0"><if>p1 p2 p3 : Prop</if><then>⊢ True ∨ (False → False → True)</then></state>||
|
<tactic>apply Or.inl</tactic><state id="1"><if>case h</if><if>p1 p2 p3 : Prop</if><then>⊢ True</then></state><tactic>apply True.intro</tactic><state id="2"><complete /></state><success />
|
true
| 2
|
<state id="0"><if>p1 p2 p3 : Prop</if><then>⊢ True ∨ (False → False) ∨ True</then></state>||
|
<tactic>apply Or.inl</tactic><state id="1"><if>case h</if><if>p1 p2 p3 : Prop</if><then>⊢ True</then></state><tactic>apply True.intro</tactic><state id="2"><complete /></state><success />
|
true
| 2
|
<state id="0"><if>p1 p2 p3 : Prop</if><then>⊢ True ∨ False ∧ (False ∨ p1)</then></state>||
|
<tactic>apply Or.inl</tactic><state id="1"><if>case h</if><if>p1 p2 p3 : Prop</if><then>⊢ True</then></state><tactic>apply True.intro</tactic><state id="2"><complete /></state><success />
|
true
| 2
|
<state id="0"><if>p1 p2 p3 : Prop</if><then>⊢ True ∨ False ∨ (False → p1)</then></state>||
|
<tactic>apply Or.inl</tactic><state id="1"><if>case h</if><if>p1 p2 p3 : Prop</if><then>⊢ True</then></state><tactic>apply True.intro</tactic><state id="2"><complete /></state><success />
|
true
| 2
|
<state id="0"><if>p1 p2 p3 : Prop</if><then>⊢ True ∨ (False ∧ False → p1)</then></state>||
|
<tactic>apply Or.inl</tactic><state id="1"><if>case h</if><if>p1 p2 p3 : Prop</if><then>⊢ True</then></state><tactic>apply True.intro</tactic><state id="2"><complete /></state><success />
|
true
| 2
|
<state id="0"><if>p1 p2 p3 : Prop</if><then>⊢ True ∨ (False → False) ∧ p1</then></state>||
|
<tactic>apply Or.inl</tactic><state id="1"><if>case h</if><if>p1 p2 p3 : Prop</if><then>⊢ True</then></state><tactic>apply True.intro</tactic><state id="2"><complete /></state><success />
|
true
| 2
|
<state id="0"><if>p1 p2 p3 : Prop</if><then>⊢ True ∨ (False → False ∧ p2)</then></state>||
|
<tactic>apply Or.inl</tactic><state id="1"><if>case h</if><if>p1 p2 p3 : Prop</if><then>⊢ True</then></state><tactic>apply True.intro</tactic><state id="2"><complete /></state><success />
|
true
| 2
|
<state id="0"><if>p1 p2 p3 : Prop</if><then>⊢ True ∨ False ∧ (False → p2)</then></state>||
|
<tactic>apply Or.inl</tactic><state id="1"><if>case h</if><if>p1 p2 p3 : Prop</if><then>⊢ True</then></state><tactic>apply True.intro</tactic><state id="2"><complete /></state><success />
|
true
| 2
|
<state id="0"><if>p1 p2 p3 : Prop</if><then>⊢ True ∨ False ∧ False ∨ p2</then></state>||
|
<tactic>apply Or.inl</tactic><state id="1"><if>case h</if><if>p1 p2 p3 : Prop</if><then>⊢ True</then></state><tactic>apply True.intro</tactic><state id="2"><complete /></state><success />
|
true
| 2
|
<state id="0"><if>p1 p2 p3 : Prop</if><then>⊢ True ∨ (False ∨ False → p2)</then></state>||
|
<tactic>apply Or.inl</tactic><state id="1"><if>case h</if><if>p1 p2 p3 : Prop</if><then>⊢ True</then></state><tactic>apply True.intro</tactic><state id="2"><complete /></state><success />
|
true
| 2
|
<state id="0"><if>p1 p2 p3 : Prop</if><then>⊢ True ∨ False ∨ False ∧ p3</then></state>||
|
<tactic>apply Or.inl</tactic><state id="1"><if>case h</if><if>p1 p2 p3 : Prop</if><then>⊢ True</then></state><tactic>apply True.intro</tactic><state id="2"><complete /></state><success />
|
true
| 2
|
<state id="0"><if>p1 p2 p3 : Prop</if><then>⊢ True ∨ (False → False ∨ p3)</then></state>||
|
<tactic>apply Or.inl</tactic><state id="1"><if>case h</if><if>p1 p2 p3 : Prop</if><then>⊢ True</then></state><tactic>apply True.intro</tactic><state id="2"><complete /></state><success />
|
true
| 2
|
<state id="0"><if>p1 p2 p3 : Prop</if><then>⊢ True ∨ (False ∧ False) ∧ p3</then></state>||
|
<tactic>apply Or.inl</tactic><state id="1"><if>case h</if><if>p1 p2 p3 : Prop</if><then>⊢ True</then></state><tactic>apply True.intro</tactic><state id="2"><complete /></state><success />
|
true
| 2
|
<state id="0"><if>p1 p2 p3 : Prop</if><then>⊢ True ∨ (False ∨ False) ∨ p3</then></state>||
|
<tactic>apply Or.inl</tactic><state id="1"><if>case h</if><if>p1 p2 p3 : Prop</if><then>⊢ True</then></state><tactic>apply True.intro</tactic><state id="2"><complete /></state><success />
|
true
| 2
|
<state id="0"><if>p1 p2 p3 : Prop</if><then>⊢ True ∨ ((False → False) → p3)</then></state>||
|
<tactic>apply Or.inl</tactic><state id="1"><if>case h</if><if>p1 p2 p3 : Prop</if><then>⊢ True</then></state><tactic>apply True.intro</tactic><state id="2"><complete /></state><success />
|
true
| 2
|
<state id="0"><if>p1 p2 p3 : Prop</if><then>⊢ True ∨ False ∧ True ∧ False</then></state>||
|
<tactic>apply Or.inl</tactic><state id="1"><if>case h</if><if>p1 p2 p3 : Prop</if><then>⊢ True</then></state><tactic>apply True.intro</tactic><state id="2"><complete /></state><success />
|
true
| 2
|
<state id="0"><if>p1 p2 p3 : Prop</if><then>⊢ True ∨ False ∨ True ∨ False</then></state>||
|
<tactic>apply Or.inl</tactic><state id="1"><if>case h</if><if>p1 p2 p3 : Prop</if><then>⊢ True</then></state><tactic>apply True.intro</tactic><state id="2"><complete /></state><success />
|
true
| 2
|
<state id="0"><if>p1 p2 p3 : Prop</if><then>⊢ True ∨ (False → True → False)</then></state>||
|
<tactic>apply Or.inl</tactic><state id="1"><if>case h</if><if>p1 p2 p3 : Prop</if><then>⊢ True</then></state><tactic>apply True.intro</tactic><state id="2"><complete /></state><success />
|
true
| 2
|
<state id="0"><if>p1 p2 p3 : Prop</if><then>⊢ True ∨ (False ∨ True) ∧ False</then></state>||
|
<tactic>apply Or.inl</tactic><state id="1"><if>case h</if><if>p1 p2 p3 : Prop</if><then>⊢ True</then></state><tactic>apply True.intro</tactic><state id="2"><complete /></state><success />
|
true
| 2
|
<state id="0"><if>p1 p2 p3 : Prop</if><then>⊢ True ∨ (False → True) ∨ False</then></state>||
|
<tactic>apply Or.inl</tactic><state id="1"><if>case h</if><if>p1 p2 p3 : Prop</if><then>⊢ True</then></state><tactic>apply True.intro</tactic><state id="2"><complete /></state><success />
|
true
| 2
|
<state id="0"><if>p1 p2 p3 : Prop</if><then>⊢ True ∨ False ∧ (True ∨ True)</then></state>||
|
<tactic>apply Or.inl</tactic><state id="1"><if>case h</if><if>p1 p2 p3 : Prop</if><then>⊢ True</then></state><tactic>apply True.intro</tactic><state id="2"><complete /></state><success />
|
true
| 2
|
<state id="0"><if>p1 p2 p3 : Prop</if><then>⊢ True ∨ False ∨ (True → True)</then></state>||
|
<tactic>apply Or.inl</tactic><state id="1"><if>case h</if><if>p1 p2 p3 : Prop</if><then>⊢ True</then></state><tactic>apply True.intro</tactic><state id="2"><complete /></state><success />
|
true
| 2
|
<state id="0"><if>p1 p2 p3 : Prop</if><then>⊢ True ∨ (False ∧ True → True)</then></state>||
|
<tactic>apply Or.inl</tactic><state id="1"><if>case h</if><if>p1 p2 p3 : Prop</if><then>⊢ True</then></state><tactic>apply True.intro</tactic><state id="2"><complete /></state><success />
|
true
| 2
|
<state id="0"><if>p1 p2 p3 : Prop</if><then>⊢ True ∨ (False → True) ∧ True</then></state>||
|
<tactic>apply Or.inl</tactic><state id="1"><if>case h</if><if>p1 p2 p3 : Prop</if><then>⊢ True</then></state><tactic>apply True.intro</tactic><state id="2"><complete /></state><success />
|
true
| 2
|
<state id="0"><if>p1 p2 p3 : Prop</if><then>⊢ True ∨ (False → True ∧ p1)</then></state>||
|
<tactic>apply Or.inl</tactic><state id="1"><if>case h</if><if>p1 p2 p3 : Prop</if><then>⊢ True</then></state><tactic>apply True.intro</tactic><state id="2"><complete /></state><success />
|
true
| 2
|
<state id="0"><if>p1 p2 p3 : Prop</if><then>⊢ True ∨ False ∧ (True → p1)</then></state>||
|
<tactic>apply Or.inl</tactic><state id="1"><if>case h</if><if>p1 p2 p3 : Prop</if><then>⊢ True</then></state><tactic>apply True.intro</tactic><state id="2"><complete /></state><success />
|
true
| 2
|
<state id="0"><if>p1 p2 p3 : Prop</if><then>⊢ True ∨ False ∧ True ∨ p1</then></state>||
|
<tactic>apply Or.inl</tactic><state id="1"><if>case h</if><if>p1 p2 p3 : Prop</if><then>⊢ True</then></state><tactic>apply True.intro</tactic><state id="2"><complete /></state><success />
|
true
| 2
|
<state id="0"><if>p1 p2 p3 : Prop</if><then>⊢ True ∨ (False ∨ True → p1)</then></state>||
|
<tactic>apply Or.inl</tactic><state id="1"><if>case h</if><if>p1 p2 p3 : Prop</if><then>⊢ True</then></state><tactic>apply True.intro</tactic><state id="2"><complete /></state><success />
|
true
| 2
|
<state id="0"><if>p1 p2 p3 : Prop</if><then>⊢ True ∨ False ∨ True ∧ p2</then></state>||
|
<tactic>apply Or.inl</tactic><state id="1"><if>case h</if><if>p1 p2 p3 : Prop</if><then>⊢ True</then></state><tactic>apply True.intro</tactic><state id="2"><complete /></state><success />
|
true
| 2
|
<state id="0"><if>p1 p2 p3 : Prop</if><then>⊢ True ∨ (False → True ∨ p2)</then></state>||
|
<tactic>apply Or.inl</tactic><state id="1"><if>case h</if><if>p1 p2 p3 : Prop</if><then>⊢ True</then></state><tactic>apply True.intro</tactic><state id="2"><complete /></state><success />
|
true
| 2
|
<state id="0"><if>p1 p2 p3 : Prop</if><then>⊢ True ∨ (False ∧ True) ∧ p2</then></state>||
|
<tactic>apply Or.inl</tactic><state id="1"><if>case h</if><if>p1 p2 p3 : Prop</if><then>⊢ True</then></state><tactic>apply True.intro</tactic><state id="2"><complete /></state><success />
|
true
| 2
|
<state id="0"><if>p1 p2 p3 : Prop</if><then>⊢ True ∨ (False ∨ True) ∨ p2</then></state>||
|
<tactic>apply Or.inl</tactic><state id="1"><if>case h</if><if>p1 p2 p3 : Prop</if><then>⊢ True</then></state><tactic>apply True.intro</tactic><state id="2"><complete /></state><success />
|
true
| 2
|
<state id="0"><if>p1 p2 p3 : Prop</if><then>⊢ True ∨ ((False → True) → p2)</then></state>||
|
<tactic>apply Or.inl</tactic><state id="1"><if>case h</if><if>p1 p2 p3 : Prop</if><then>⊢ True</then></state><tactic>apply True.intro</tactic><state id="2"><complete /></state><success />
|
true
| 2
|
<state id="0"><if>p1 p2 p3 : Prop</if><then>⊢ True ∨ False ∧ True ∧ p3</then></state>||
|
<tactic>apply Or.inl</tactic><state id="1"><if>case h</if><if>p1 p2 p3 : Prop</if><then>⊢ True</then></state><tactic>apply True.intro</tactic><state id="2"><complete /></state><success />
|
true
| 2
|
<state id="0"><if>p1 p2 p3 : Prop</if><then>⊢ True ∨ False ∨ True ∨ p3</then></state>||
|
<tactic>apply Or.inl</tactic><state id="1"><if>case h</if><if>p1 p2 p3 : Prop</if><then>⊢ True</then></state><tactic>apply True.intro</tactic><state id="2"><complete /></state><success />
|
true
| 2
|
<state id="0"><if>p1 p2 p3 : Prop</if><then>⊢ True ∨ (False ∨ True) ∧ p3</then></state>||
|
<tactic>apply Or.inl</tactic><state id="1"><if>case h</if><if>p1 p2 p3 : Prop</if><then>⊢ True</then></state><tactic>apply True.intro</tactic><state id="2"><complete /></state><success />
|
true
| 2
|
<state id="0"><if>p1 p2 p3 : Prop</if><then>⊢ True ∨ (False → True → p3)</then></state>||
|
<tactic>apply Or.inl</tactic><state id="1"><if>case h</if><if>p1 p2 p3 : Prop</if><then>⊢ True</then></state><tactic>apply True.intro</tactic><state id="2"><complete /></state><success />
|
true
| 2
|
<state id="0"><if>p1 p2 p3 : Prop</if><then>⊢ True ∨ (False → True) ∨ p3</then></state>||
|
<tactic>apply Or.inl</tactic><state id="1"><if>case h</if><if>p1 p2 p3 : Prop</if><then>⊢ True</then></state><tactic>apply True.intro</tactic><state id="2"><complete /></state><success />
|
true
| 2
|
<state id="0"><if>p1 p2 p3 : Prop</if><then>⊢ True ∨ False ∧ (p1 ∨ False)</then></state>||
|
<tactic>apply Or.inl</tactic><state id="1"><if>case h</if><if>p1 p2 p3 : Prop</if><then>⊢ True</then></state><tactic>apply True.intro</tactic><state id="2"><complete /></state><success />
|
true
| 2
|
<state id="0"><if>p1 p2 p3 : Prop</if><then>⊢ True ∨ False ∨ (p1 → False)</then></state>||
|
<tactic>apply Or.inl</tactic><state id="1"><if>case h</if><if>p1 p2 p3 : Prop</if><then>⊢ True</then></state><tactic>apply True.intro</tactic><state id="2"><complete /></state><success />
|
true
| 2
|
<state id="0"><if>p1 p2 p3 : Prop</if><then>⊢ True ∨ (False ∧ p1 → False)</then></state>||
|
<tactic>apply Or.inl</tactic><state id="1"><if>case h</if><if>p1 p2 p3 : Prop</if><then>⊢ True</then></state><tactic>apply True.intro</tactic><state id="2"><complete /></state><success />
|
true
| 2
|
<state id="0"><if>p1 p2 p3 : Prop</if><then>⊢ True ∨ (False → p1) ∧ False</then></state>||
|
<tactic>apply Or.inl</tactic><state id="1"><if>case h</if><if>p1 p2 p3 : Prop</if><then>⊢ True</then></state><tactic>apply True.intro</tactic><state id="2"><complete /></state><success />
|
true
| 2
|
<state id="0"><if>p1 p2 p3 : Prop</if><then>⊢ True ∨ (False → p1 ∧ True)</then></state>||
|
<tactic>apply Or.inl</tactic><state id="1"><if>case h</if><if>p1 p2 p3 : Prop</if><then>⊢ True</then></state><tactic>apply True.intro</tactic><state id="2"><complete /></state><success />
|
true
| 2
|
<state id="0"><if>p1 p2 p3 : Prop</if><then>⊢ True ∨ False ∧ (p1 → True)</then></state>||
|
<tactic>apply Or.inl</tactic><state id="1"><if>case h</if><if>p1 p2 p3 : Prop</if><then>⊢ True</then></state><tactic>apply True.intro</tactic><state id="2"><complete /></state><success />
|
true
| 2
|
<state id="0"><if>p1 p2 p3 : Prop</if><then>⊢ True ∨ False ∧ p1 ∨ True</then></state>||
|
<tactic>apply Or.inl</tactic><state id="1"><if>case h</if><if>p1 p2 p3 : Prop</if><then>⊢ True</then></state><tactic>apply True.intro</tactic><state id="2"><complete /></state><success />
|
true
| 2
|
<state id="0"><if>p1 p2 p3 : Prop</if><then>⊢ True ∨ (False ∨ p1 → True)</then></state>||
|
<tactic>apply Or.inl</tactic><state id="1"><if>case h</if><if>p1 p2 p3 : Prop</if><then>⊢ True</then></state><tactic>apply True.intro</tactic><state id="2"><complete /></state><success />
|
true
| 2
|
<state id="0"><if>p1 p2 p3 : Prop</if><then>⊢ True ∨ False ∨ p1 ∧ p1</then></state>||
|
<tactic>apply Or.inl</tactic><state id="1"><if>case h</if><if>p1 p2 p3 : Prop</if><then>⊢ True</then></state><tactic>apply True.intro</tactic><state id="2"><complete /></state><success />
|
true
| 2
|
<state id="0"><if>p1 p2 p3 : Prop</if><then>⊢ True ∨ (False ∧ p1) ∧ p1</then></state>||
|
<tactic>apply Or.inl</tactic><state id="1"><if>case h</if><if>p1 p2 p3 : Prop</if><then>⊢ True</then></state><tactic>apply True.intro</tactic><state id="2"><complete /></state><success />
|
true
| 2
|
<state id="0"><if>p1 p2 p3 : Prop</if><then>⊢ True ∨ (False → p1 ∨ p1)</then></state>||
|
<tactic>apply Or.inl</tactic><state id="1"><if>case h</if><if>p1 p2 p3 : Prop</if><then>⊢ True</then></state><tactic>apply True.intro</tactic><state id="2"><complete /></state><success />
|
true
| 2
|
<state id="0"><if>p1 p2 p3 : Prop</if><then>⊢ True ∨ (False ∨ p1) ∨ p1</then></state>||
|
<tactic>apply Or.inl</tactic><state id="1"><if>case h</if><if>p1 p2 p3 : Prop</if><then>⊢ True</then></state><tactic>apply True.intro</tactic><state id="2"><complete /></state><success />
|
true
| 2
|
<state id="0"><if>p1 p2 p3 : Prop</if><then>⊢ True ∨ ((False → p1) → p1)</then></state>||
|
<tactic>apply Or.inl</tactic><state id="1"><if>case h</if><if>p1 p2 p3 : Prop</if><then>⊢ True</then></state><tactic>apply True.intro</tactic><state id="2"><complete /></state><success />
|
true
| 2
|
<state id="0"><if>p1 p2 p3 : Prop</if><then>⊢ True ∨ False ∧ p1 ∧ p2</then></state>||
|
<tactic>apply Or.inl</tactic><state id="1"><if>case h</if><if>p1 p2 p3 : Prop</if><then>⊢ True</then></state><tactic>apply True.intro</tactic><state id="2"><complete /></state><success />
|
true
| 2
|
<state id="0"><if>p1 p2 p3 : Prop</if><then>⊢ True ∨ False ∨ p1 ∨ p2</then></state>||
|
<tactic>apply Or.inl</tactic><state id="1"><if>case h</if><if>p1 p2 p3 : Prop</if><then>⊢ True</then></state><tactic>apply True.intro</tactic><state id="2"><complete /></state><success />
|
true
| 2
|
<state id="0"><if>p1 p2 p3 : Prop</if><then>⊢ True ∨ (False → p1 → p2)</then></state>||
|
<tactic>apply Or.inl</tactic><state id="1"><if>case h</if><if>p1 p2 p3 : Prop</if><then>⊢ True</then></state><tactic>apply True.intro</tactic><state id="2"><complete /></state><success />
|
true
| 2
|
<state id="0"><if>p1 p2 p3 : Prop</if><then>⊢ True ∨ (False ∨ p1) ∧ p2</then></state>||
|
<tactic>apply Or.inl</tactic><state id="1"><if>case h</if><if>p1 p2 p3 : Prop</if><then>⊢ True</then></state><tactic>apply True.intro</tactic><state id="2"><complete /></state><success />
|
true
| 2
|
<state id="0"><if>p1 p2 p3 : Prop</if><then>⊢ True ∨ (False → p1) ∨ p2</then></state>||
|
<tactic>apply Or.inl</tactic><state id="1"><if>case h</if><if>p1 p2 p3 : Prop</if><then>⊢ True</then></state><tactic>apply True.intro</tactic><state id="2"><complete /></state><success />
|
true
| 2
|
<state id="0"><if>p1 p2 p3 : Prop</if><then>⊢ True ∨ False ∧ (p1 ∨ p3)</then></state>||
|
<tactic>apply Or.inl</tactic><state id="1"><if>case h</if><if>p1 p2 p3 : Prop</if><then>⊢ True</then></state><tactic>apply True.intro</tactic><state id="2"><complete /></state><success />
|
true
| 2
|
<state id="0"><if>p1 p2 p3 : Prop</if><then>⊢ True ∨ False ∨ (p1 → p3)</then></state>||
|
<tactic>apply Or.inl</tactic><state id="1"><if>case h</if><if>p1 p2 p3 : Prop</if><then>⊢ True</then></state><tactic>apply True.intro</tactic><state id="2"><complete /></state><success />
|
true
| 2
|
<state id="0"><if>p1 p2 p3 : Prop</if><then>⊢ True ∨ (False ∧ p1 → p3)</then></state>||
|
<tactic>apply Or.inl</tactic><state id="1"><if>case h</if><if>p1 p2 p3 : Prop</if><then>⊢ True</then></state><tactic>apply True.intro</tactic><state id="2"><complete /></state><success />
|
true
| 2
|
<state id="0"><if>p1 p2 p3 : Prop</if><then>⊢ True ∨ (False → p1) ∧ p3</then></state>||
|
<tactic>apply Or.inl</tactic><state id="1"><if>case h</if><if>p1 p2 p3 : Prop</if><then>⊢ True</then></state><tactic>apply True.intro</tactic><state id="2"><complete /></state><success />
|
true
| 2
|
<state id="0"><if>p1 p2 p3 : Prop</if><then>⊢ True ∨ (False → p2 ∧ False)</then></state>||
|
<tactic>apply Or.inl</tactic><state id="1"><if>case h</if><if>p1 p2 p3 : Prop</if><then>⊢ True</then></state><tactic>apply True.intro</tactic><state id="2"><complete /></state><success />
|
true
| 2
|
<state id="0"><if>p1 p2 p3 : Prop</if><then>⊢ True ∨ False ∧ p2 ∨ False</then></state>||
|
<tactic>apply Or.inl</tactic><state id="1"><if>case h</if><if>p1 p2 p3 : Prop</if><then>⊢ True</then></state><tactic>apply True.intro</tactic><state id="2"><complete /></state><success />
|
true
| 2
|
<state id="0"><if>p1 p2 p3 : Prop</if><then>⊢ True ∨ False ∧ (p2 → False)</then></state>||
|
<tactic>apply Or.inl</tactic><state id="1"><if>case h</if><if>p1 p2 p3 : Prop</if><then>⊢ True</then></state><tactic>apply True.intro</tactic><state id="2"><complete /></state><success />
|
true
| 2
|
<state id="0"><if>p1 p2 p3 : Prop</if><then>⊢ True ∨ (False ∨ p2 → False)</then></state>||
|
<tactic>apply Or.inl</tactic><state id="1"><if>case h</if><if>p1 p2 p3 : Prop</if><then>⊢ True</then></state><tactic>apply True.intro</tactic><state id="2"><complete /></state><success />
|
true
| 2
|
<state id="0"><if>p1 p2 p3 : Prop</if><then>⊢ True ∨ False ∨ p2 ∧ True</then></state>||
|
<tactic>apply Or.inl</tactic><state id="1"><if>case h</if><if>p1 p2 p3 : Prop</if><then>⊢ True</then></state><tactic>apply True.intro</tactic><state id="2"><complete /></state><success />
|
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.