Expression of type ExprTuple

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 ExprTuple, 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 = ExprTuple(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(\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]\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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