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 Conditional, ExprTuple, Lambda, i, x
from proveit.core_expr_types import Len, f_1_to_i, range_1_to_ip1
from proveit.logic import Equals, InSet
from proveit.numbers import Natural

# build up the expression from sub-expressions
expr = ExprTuple(Lambda(i, Conditional(Equals(Len(operands = [f_1_to_i, x]), Len(operands = [range_1_to_ip1])), InSet(i, Natural))))

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(i \mapsto \left\{|\left(f\left(1\right), f\left(2\right), \ldots, f\left(i\right), x\right)| = |\left(1, 2, \ldots, \left(i + 1\right)\right)| \textrm{ if } i \in \mathbb{N}\right..\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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