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In [1]:
import proveit
from proveit import defaults
theory = proveit.Theory() # the theorem's theory
In [2]:
%proving singular_range_reduction
With these allowed/disallowed theorem/theory presumptions (e.g., to avoid circular dependencies), we begin our proof of
singular_range_reduction:
(see dependencies)
In [3]:
defaults.assumptions = singular_range_reduction.conditions
defaults.assumptions:
In [4]:
i_eq_j = defaults.assumptions[0]
i_eq_j:
In [5]:
i_eq_j.derive_reversed().substitution(singular_range_reduction.instance_expr.lhs)
singular_range_reduction may now be readily provable (assuming required theorems are usable).  Simply execute "%qed".
In [6]:
%qed
proveit.core_expr_types.tuples.singular_range_reduction has been proven.
Out[6]:
 step typerequirementsstatement
0generalization1  ⊢  
1instantiation2, 3  ⊢  
  : , : , :
2axiom  ⊢  
 proveit.logic.equality.substitution
3instantiation4, 5  ⊢  
  : , :
4theorem  ⊢  
 proveit.logic.equality.equals_reversal
5assumption  ⊢