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, f, i
from proveit.core_expr_types import Len, f_1_to_i, range_1_to_i
from proveit.logic import Equals, Forall, InSet
from proveit.numbers import Natural

# build up the expression from sub-expressions
expr = Lambda(i, Conditional(Forall(instance_param_or_params = [f], instance_expr = Equals(Len(operands = [f_1_to_i]), Len(operands = [range_1_to_i]))), 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\{\forall_{f}~\left(|\left(f\left(1\right), f\left(2\right), \ldots, f\left(i\right)\right)| = |\left(1, 2, \ldots, i\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: 25 body: 2
1	ExprTuple	25
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operand: 9
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	9
7	Literal
8	ExprTuple	25, 10
9	Lambda	parameter: 27 body: 12
10	Literal
11	ExprTuple	27
12	Operation	operator: 13 operands: 14
13	Literal
14	ExprTuple	15, 16
15	Operation	operator: 18 operands: 17
16	Operation	operator: 18 operands: 19
17	ExprTuple	20
18	Literal
19	ExprTuple	21
20	ExprRange	lambda_map: 22 start_index: 24 end_index: 25
21	ExprRange	lambda_map: 23 start_index: 24 end_index: 25
22	Lambda	parameter: 29 body: 26
23	Lambda	parameter: 29 body: 29
24	Literal
25	Variable
26	Operation	operator: 27 operand: 29
27	Variable
28	ExprTuple	29
29	Variable