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, x
from proveit.core_expr_types import Len, f_1_to_i, range_1_to_ip1
from proveit.logic import Equals, Forall
from proveit.numbers import Natural

# build up the expression from sub-expressions
expr = Lambda([f, x], Forall(instance_param_or_params = [i], instance_expr = Equals(Len(operands = [f_1_to_i, x]), Len(operands = [range_1_to_ip1])), domain = 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 \in \mathbb{N}}~\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)|\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	29, 21
2	Operation	operator: 3 operand: 5
3	Literal
4	ExprTuple	5
5	Lambda	parameter: 31 body: 7
6	ExprTuple	31
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	31, 16
14	Operation	operator: 18 operands: 17
15	Operation	operator: 18 operands: 19
16	Literal
17	ExprTuple	20, 21
18	Literal
19	ExprTuple	22
20	ExprRange	lambda_map: 23 start_index: 32 end_index: 31
21	Variable
22	ExprRange	lambda_map: 24 start_index: 32 end_index: 25
23	Lambda	parameter: 33 body: 26
24	Lambda	parameter: 33 body: 33
25	Operation	operator: 27 operands: 28
26	Operation	operator: 29 operand: 33
27	Literal
28	ExprTuple	31, 32
29	Variable
30	ExprTuple	33
31	Variable
32	Literal
33	Variable