Proof of proveit.logic.booleans.disjunction.unary_or_reduction theorem¶
In [1]:
import proveit
from proveit.logic import TRUE, FALSE
from proveit import A
from proveit.logic.booleans.disjunction import unary_or_lemma
from proveit.logic.booleans.disjunction import or_f_t, or_f_f
theory = proveit.Theory() # the theorem's theory
In [2]:
%proving unary_or_reduction
With these allowed/disallowed theorem/theory presumptions (e.g., to avoid circular dependencies), we begin our proof of
unary_or_reduction:
(see dependencies)
unary_or_reduction:
(see dependencies)
In [3]:
base_case_t_r_u_e = unary_or_lemma.instantiate({A:TRUE})
base_case_t_r_u_e: ⊢ 
In [4]:
base_case_f_a_l_s_e = unary_or_lemma.instantiate({A:FALSE})
base_case_f_a_l_s_e: ⊢ 
In [5]:
base_case_t_r_u_e.sub_left_side_into(or_f_t)
In [6]:
base_case_f_a_l_s_e.sub_left_side_into(or_f_f)
In [7]:
%qed
Out[7]:
| step type | requirements | statement | ||
|---|---|---|---|---|
| 0 | instantiation | 1, 2, 3 | ⊢ | |
 :  ,  : | ||||
| 1 | conjecture | ⊢  | ||
| proveit.logic.booleans.forall_over_bool_by_cases | ||||
| 2 | instantiation | 6, 4, 5* | ⊢ | |
:  | ||||
| 3 | instantiation | 6, 7, 8* | ⊢ | |
:  | ||||
| 4 | conjecture | ⊢  | ||
| proveit.logic.booleans.true_is_bool | ||||
| 5 | axiom | ⊢  | ||
| proveit.logic.booleans.disjunction.or_f_t | ||||
| 6 | conjecture | ⊢  | ||
| proveit.logic.booleans.disjunction.unary_or_lemma | ||||
| 7 | conjecture | ⊢  | ||
| proveit.logic.booleans.false_is_bool | ||||
| 8 | axiom | ⊢  | ||
| proveit.logic.booleans.disjunction.or_f_f | ||||
| *equality replacement requirements | ||||