Proof of proveit.physics.quantum.QPE._mod_add_closure theorem

import proveit
from proveit import defaults
from proveit import a, b
from proveit.logic import InSet
from proveit.numbers import Add, Integer
from proveit.numbers.modular import mod_int_closure
from proveit.physics.quantum.QPE import _two_pow_t            # common
from proveit.physics.quantum.QPE import _mod_add_def          # axioms
from proveit.physics.quantum.QPE import _two_pow_t_is_nat_pos # theorems
theory = proveit.Theory() # the theorem's theory

%proving _mod_add_closure

With these allowed/disallowed theorem/theory presumptions (e.g., to avoid circular dependencies), we begin our proof of
_mod_add_closure:
(see dependencies)

defaults.assumptions = _mod_add_closure.conditions

defaults.assumptions:

_mod_add_def

 ⊢  

mod_add_def_inst = _mod_add_def.instantiate({a:a, b:b})

mod_add_def_inst: ,  ⊢  

mod_add_def_inst.rhs.deduce_in_interval()

,  ⊢  

%qed

proveit.physics.quantum.QPE._mod_add_closure has been proven.

	step type	requirements	statement
0	generalization	1	⊢
1	instantiation	2, 3, 4	,  ⊢
	: , : , :
2	theorem		⊢
	proveit.logic.equality.sub_left_side_into
3	instantiation	5, 6, 7	,  ⊢
	: , :
4	instantiation	8, 10, 11	,  ⊢
	: , :
5	conjecture		⊢
	proveit.numbers.modular.mod_natpos_in_interval
6	instantiation	9, 10, 11	,  ⊢
	: , :
7	conjecture		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
8	axiom		⊢
	proveit.physics.quantum.QPE._mod_add_def
9	conjecture		⊢
	proveit.numbers.addition.add_int_closure_bin
10	assumption		⊢
11	assumption		⊢