Expression of type ExprTuple

from the theory of proveit.core_expr_types.tuples

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 ExprTuple, i, j, k
from proveit.core_expr_types import f_i_to_j, fk, g_i_to_j, gk
from proveit.logic import Equals, Forall
from proveit.numbers import Interval

# build up the expression from sub-expressions
expr = ExprTuple(Forall(instance_param_or_params = [k], instance_expr = Equals(fk, gk), domain = Interval(i, j)), Equals([f_i_to_j], [g_i_to_j]))

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_{k \in \{i~\ldotp \ldotp~j\}}~\left(f\left(k\right) = g\left(k\right)\right), \left(f\left(i\right), f\left(i + 1\right), \ldots, f\left(j\right)\right) = \left(g\left(i\right), g\left(i + 1\right), \ldots, g\left(j\right)\right)\right)

stored_expr.style_options()

name	description	default	current value	related methods
wrap_positions	position(s) at which wrapping is to occur; 'n' is after the nth comma.	()	()	('with_wrapping_at',)
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	left	left	('with_justification',)

# display the expression information
stored_expr.expr_info()

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