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 ExprRange, ExprTuple, IndexedVar, Variable, a, b, m
from proveit.logic import Equals, Forall, InSet
from proveit.numbers import Add, NaturalPos, one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = IndexedVar(a, sub_expr1)
sub_expr3 = IndexedVar(b, sub_expr1)
sub_expr4 = ExprRange(sub_expr1, sub_expr2, one, m)
sub_expr5 = ExprRange(sub_expr1, sub_expr3, one, m)
sub_expr6 = Equals(sub_expr2, sub_expr3)
expr = ExprTuple(InSet(m, NaturalPos), Forall(instance_param_or_params = [sub_expr4, sub_expr5], instance_expr = Equals([sub_expr4], [sub_expr5]), condition = ExprRange(sub_expr1, sub_expr6, one, m)), ExprRange(sub_expr1, sub_expr6, one, Add(m, one)))

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(m \in \mathbb{N}^+, \forall_{a_{1}, a_{2}, \ldots, a_{m}, b_{1}, b_{2}, \ldots, b_{m}~|~\left(a_{1} = b_{1}\right), \left(a_{2} = b_{2}\right), \ldots, \left(a_{m} = b_{m}\right)}~\left(\left(a_{1}, a_{2}, \ldots, a_{m}\right) = \left(b_{1}, b_{2}, \ldots, b_{m}\right)\right),\left(a_{1} = b_{1}\right), \left(a_{2} = b_{2}\right), \ldots, \left(a_{m + 1} = b_{m + 1}\right)\right)

stored_expr.style_options()

name	description	default	current value	related methods
wrap_positions	position(s) at which wrapping is to occur; 'n' is after the nth comma.	()	()	('with_wrapping_at',)
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	left	left	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1, 2, 3
1	Operation	operator: 4 operands: 5
2	Operation	operator: 6 operand: 10
3	ExprRange	lambda_map: 25 start_index: 28 end_index: 8
4	Literal
5	ExprTuple	29, 9
6	Literal
7	ExprTuple	10
8	Operation	operator: 11 operands: 12
9	Literal
10	Lambda	parameters: 13 body: 14
11	Literal
12	ExprTuple	29, 28
13	ExprTuple	23, 24
14	Conditional	value: 15 condition: 16
15	Operation	operator: 31 operands: 17
16	Operation	operator: 18 operands: 19
17	ExprTuple	20, 21
18	Literal
19	ExprTuple	22
20	ExprTuple	23
21	ExprTuple	24
22	ExprRange	lambda_map: 25 start_index: 28 end_index: 29
23	ExprRange	lambda_map: 26 start_index: 28 end_index: 29
24	ExprRange	lambda_map: 27 start_index: 28 end_index: 29
25	Lambda	parameter: 38 body: 30
26	Lambda	parameter: 38 body: 33
27	Lambda	parameter: 38 body: 34
28	Literal
29	Variable
30	Operation	operator: 31 operands: 32
31	Literal
32	ExprTuple	33, 34
33	IndexedVar	variable: 35 index: 38
34	IndexedVar	variable: 36 index: 38
35	Variable
36	Variable
37	ExprTuple	38
38	Variable