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
from proveit.core_expr_types import Len, f_1_to_i, range_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]), Len(operands = [range_1_to_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)| = |\left(1, 2, \ldots, i\right)|\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameter: 17 body: 2
1	ExprTuple	17
2	Operation	operator: 3 operands: 4
3	Literal
4	ExprTuple	5, 6
5	Operation	operator: 8 operands: 7
6	Operation	operator: 8 operands: 9
7	ExprTuple	10
8	Literal
9	ExprTuple	11
10	ExprRange	lambda_map: 12 start_index: 14 end_index: 15
11	ExprRange	lambda_map: 13 start_index: 14 end_index: 15
12	Lambda	parameter: 19 body: 16
13	Lambda	parameter: 19 body: 19
14	Literal
15	Variable
16	Operation	operator: 17 operand: 19
17	Variable
18	ExprTuple	19
19	Variable