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 Lambda, f, i, j, x
from proveit.core_expr_types import Len, f_i_to_j, range_i_to_jp1
from proveit.logic import Equals, Forall, InSet
from proveit.numbers import Natural

# build up the expression from sub-expressions
expr = Lambda([f, x], Forall(instance_param_or_params = [i, j], instance_expr = Equals(Len(operands = [f_i_to_j, x]), Len(operands = [range_i_to_jp1])), condition = InSet(Len(operands = [f_i_to_j]), 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(f, x\right) \mapsto \left[\forall_{i, j~|~|\left(f\left(i\right), f\left(i + 1\right), \ldots, f\left(j\right)\right)| \in \mathbb{N}}~\left(|\left(f\left(i\right), f\left(i + 1\right), \ldots, f\left(j\right), x\right)| = |\left(i, \left(i + 1\right), \ldots, \left(j + 1\right)\right)|\right)\right]

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameters: 1 body: 2
1	ExprTuple	34, 22
2	Operation	operator: 3 operand: 5
3	Literal
4	ExprTuple	5
5	Lambda	parameters: 6 body: 7
6	ExprTuple	28, 32
7	Conditional	value: 8 condition: 9
8	Operation	operator: 10 operands: 11
9	Operation	operator: 12 operands: 13
10	Literal
11	ExprTuple	14, 15
12	Literal
13	ExprTuple	16, 17
14	Operation	operator: 20 operands: 18
15	Operation	operator: 20 operands: 19
16	Operation	operator: 20 operands: 21
17	Literal
18	ExprTuple	24, 22
19	ExprTuple	23
20	Literal
21	ExprTuple	24
22	Variable
23	ExprRange	lambda_map: 25 start_index: 28 end_index: 26
24	ExprRange	lambda_map: 27 start_index: 28 end_index: 32
25	Lambda	parameter: 36 body: 36
26	Operation	operator: 29 operands: 30
27	Lambda	parameter: 36 body: 31
28	Variable
29	Literal
30	ExprTuple	32, 33
31	Operation	operator: 34 operand: 36
32	Variable
33	Literal
34	Variable
35	ExprTuple	36
36	Variable