Expression of type Implies

from the theory of proveit.logic.booleans.conjunction

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, Function, Q, Variable, j, k
from proveit.logic import And, Forall, Implies
from proveit.numbers import Interval

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = [sub_expr1]
sub_expr3 = Function(Q, sub_expr2)
expr = Implies(Forall(instance_param_or_params = sub_expr2, instance_expr = sub_expr3, domain = Interval(j, k)), And(ExprRange(sub_expr1, sub_expr3, j, k)))

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 \{j~\ldotp \ldotp~k\}}~Q\left({_{-}a}\right)\right] \Rightarrow \left(Q\left(j\right) \land  Q\left(j + 1\right) \land  \ldots \land  Q\left(k\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: 20 body: 11
10	ExprRange	lambda_map: 12 start_index: 23 end_index: 24
11	Conditional	value: 14 condition: 13
12	Lambda	parameter: 20 body: 14
13	Operation	operator: 15 operands: 16
14	Operation	operator: 17 operand: 20
15	Literal
16	ExprTuple	20, 19
17	Variable
18	ExprTuple	20
19	Operation	operator: 21 operands: 22
20	Variable
21	Literal
22	ExprTuple	23, 24
23	Variable
24	Variable