Expression of type Lambda

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, 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 = 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())

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..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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