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 And, Equals, Forall, Implies
from proveit.numbers import Add, Interval, Neg, one, two, zero

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = Add(Neg(t), two)
sub_expr3 = Equals(Add(sub_expr1, t), Add(Add(sub_expr1, Neg(one), t), one))
expr = Implies(Forall(instance_param_or_params = [sub_expr1], instance_expr = sub_expr3, domain = Interval(sub_expr2, zero)), And(ExprRange(sub_expr1, sub_expr3, sub_expr2, zero)))

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 \{-t + 2~\ldotp \ldotp~0\}}~\left(\left({_{-}a} + t\right) = \left(\left({_{-}a} - 1 + t\right) + 1\right)\right)\right] \Rightarrow \left(\left(\left(\left(-t + 2\right) + t\right) = \left(\left(\left(-t + 2\right) - 1 + t\right) + 1\right)\right) \land  \left(\left(\left(-t + 3\right) + t\right) = \left(\left(\left(-t + 3\right) - 1 + t\right) + 1\right)\right) \land  \ldots \land  \left(\left(0 + t\right) = \left(\left(0 - 1 + t\right) + 1\right)\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: 9
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	9
7	Literal
8	ExprTuple	10
9	Lambda	parameter: 35 body: 11
10	ExprRange	lambda_map: 12 start_index: 27 end_index: 28
11	Conditional	value: 15 condition: 13
12	Lambda	parameter: 35 body: 15
13	Operation	operator: 16 operands: 17
14	ExprTuple	35
15	Operation	operator: 18 operands: 19
16	Literal
17	ExprTuple	35, 20
18	Literal
19	ExprTuple	21, 22
20	Operation	operator: 23 operands: 24
21	Operation	operator: 31 operands: 25
22	Operation	operator: 31 operands: 26
23	Literal
24	ExprTuple	27, 28
25	ExprTuple	35, 40
26	ExprTuple	29, 41
27	Operation	operator: 31 operands: 30
28	Literal
29	Operation	operator: 31 operands: 32
30	ExprTuple	33, 34
31	Literal
32	ExprTuple	35, 36, 40
33	Operation	operator: 38 operand: 40
34	Literal
35	Variable
36	Operation	operator: 38 operand: 41
37	ExprTuple	40
38	Literal
39	ExprTuple	41
40	Variable
41	Literal