Expression of type Implies

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 ExprRange, Variable, t
from proveit.logic import Equals, Forall, Implies
from proveit.numbers import Add, Interval, Neg, one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = Add(Add(sub_expr1, Add(Neg(t), one)), Neg(one), t)
expr = Implies(Forall(instance_param_or_params = [sub_expr1], instance_expr = Equals(sub_expr2, sub_expr1), domain = Interval(one, t)), Equals([ExprRange(sub_expr1, sub_expr2, one, t)], [ExprRange(sub_expr1, sub_expr1, 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())

\left[\forall_{{_{-}a} \in \{1~\ldotp \ldotp~t\}}~\left(\left(\left({_{-}a} + \left(-t + 1\right)\right) - 1 + t\right) = {_{-}a}\right)\right] \Rightarrow \left(\left(\left(\left(1 + \left(-t + 1\right)\right) - 1 + t\right), \left(\left(2 + \left(-t + 1\right)\right) - 1 + t\right), \ldots, \left(\left(t + \left(-t + 1\right)\right) - 1 + t\right)\right) = \left(1, 2, \ldots, t\right)\right)

stored_expr.style_options()

name	description	default	current value	related methods
operation	'infix' or 'function' style formatting	infix	infix
wrap_positions	position(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.	()	()	('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	center	center	('with_justification',)
direction	Direction of the relation (normal or reversed)	normal	normal	('with_direction_reversed', 'is_reversed')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 1 operands: 2
1	Literal
2	ExprTuple	3, 4
3	Operation	operator: 5 operand: 8
4	Operation	operator: 18 operands: 7
5	Literal
6	ExprTuple	8
7	ExprTuple	9, 10
8	Lambda	parameter: 32 body: 11
9	ExprTuple	12
10	ExprTuple	13
11	Conditional	value: 14 condition: 15
12	ExprRange	lambda_map: 16 start_index: 37 end_index: 40
13	ExprRange	lambda_map: 17 start_index: 37 end_index: 40
14	Operation	operator: 18 operands: 19
15	Operation	operator: 20 operands: 21
16	Lambda	parameter: 32 body: 23
17	Lambda	parameter: 32 body: 32
18	Literal
19	ExprTuple	23, 32
20	Literal
21	ExprTuple	32, 24
22	ExprTuple	32
23	Operation	operator: 34 operands: 25
24	Operation	operator: 26 operands: 27
25	ExprTuple	28, 29, 40
26	Literal
27	ExprTuple	37, 40
28	Operation	operator: 34 operands: 30
29	Operation	operator: 38 operand: 37
30	ExprTuple	32, 33
31	ExprTuple	37
32	Variable
33	Operation	operator: 34 operands: 35
34	Literal
35	ExprTuple	36, 37
36	Operation	operator: 38 operand: 40
37	Literal
38	Literal
39	ExprTuple	40
40	Variable