Expression of type Forall

from the theory of proveit.physics.quantum.QPE

import proveit
# Automation is not needed when building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import Variable, t
from proveit.logic import Equals, Forall
from proveit.numbers import Add, Interval, Neg, one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Forall(instance_param_or_params = [sub_expr1], instance_expr = Equals(Add(Add(sub_expr1, Add(Neg(t), one)), Neg(one), t), sub_expr1), domain = Interval(one, t))

expr:

# check that the built expression is the same as the stored expression
assert expr == stored_expr
assert expr._style_id == stored_expr._style_id
print("Passed sanity check: expr matches stored_expr")

Passed sanity check: expr matches stored_expr

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\forall_{{_{-}a} \in \{1~\ldotp \ldotp~t\}}~\left(\left(\left({_{-}a} + \left(-t + 1\right)\right) - 1 + t\right) = {_{-}a}\right)

stored_expr.style_options()

name	description	default	current value	related methods
with_wrapping	If 'True', wrap the Expression after the parameters	None	None/False	('with_wrapping',)
condition_wrapping	Wrap 'before' or 'after' the condition (or None).	None	None/False	('with_wrap_after_condition', 'with_wrap_before_condition')
wrap_params	If 'True', wraps every two parameters AND wraps the Expression after the parameters	None	None/False	('with_params',)
justification	justify to the 'left', 'center', or 'right' in the array cells	center	center	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 1 operand: 3
1	Literal
2	ExprTuple	3
3	Lambda	parameter: 21 body: 5
4	ExprTuple	21
5	Conditional	value: 6 condition: 7
6	Operation	operator: 8 operands: 9
7	Operation	operator: 10 operands: 11
8	Literal
9	ExprTuple	12, 21
10	Literal
11	ExprTuple	21, 13
12	Operation	operator: 23 operands: 14
13	Operation	operator: 15 operands: 16
14	ExprTuple	17, 18, 29
15	Literal
16	ExprTuple	26, 29
17	Operation	operator: 23 operands: 19
18	Operation	operator: 27 operand: 26
19	ExprTuple	21, 22
20	ExprTuple	26
21	Variable
22	Operation	operator: 23 operands: 24
23	Literal
24	ExprTuple	25, 26
25	Operation	operator: 27 operand: 29
26	Literal
27	Literal
28	ExprTuple	29
29	Variable