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
from proveit.core_expr_types import Len, f_1_to_i
from proveit.logic import Equals

# build up the expression from sub-expressions
expr = Lambda(f, Equals(Len(operands = [f_1_to_i]), i))

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())

f \mapsto \left(|\left(f\left(1\right), f\left(2\right), \ldots, f\left(i\right)\right)| = i\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameter: 13 body: 2
1	ExprTuple	13
2	Operation	operator: 3 operands: 4
3	Literal
4	ExprTuple	5, 11
5	Operation	operator: 6 operands: 7
6	Literal
7	ExprTuple	8
8	ExprRange	lambda_map: 9 start_index: 10 end_index: 11
9	Lambda	parameter: 15 body: 12
10	Literal
11	Variable
12	Operation	operator: 13 operand: 15
13	Variable
14	ExprTuple	15
15	Variable