Expression of type Conditional

from the theory of proveit.core_expr_types.expr_arrays

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, ExprArray, i, j
from proveit.core_expr_types import a_1_to_i, b_1_to_j
from proveit.logic import And, Forall, InSet, NotEquals
from proveit.numbers import Natural

# build up the expression from sub-expressions
expr = Conditional(Forall(instance_param_or_params = [a_1_to_i, b_1_to_j], instance_expr = NotEquals(ExprArray(a_1_to_i), ExprArray(b_1_to_j))), And(InSet(i, Natural), InSet(j, Natural), NotEquals(i, j)))

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\{\forall_{a_{1}, a_{2}, \ldots, a_{i}, b_{1}, b_{2}, \ldots, b_{j}}~\left(\left(\begin{array}{c} 
 \multicolumn{1}{c}{\begin{array}{lcr} \leftarrow & a_{1} & \rightarrow \end{array}} \\
\multicolumn{1}{c}{\begin{array}{lcr} \leftarrow & a_{2} & \rightarrow \end{array}} \\
\multicolumn{1}{c}{\begin{array}{lcr} \leftarrow & \vdots & \rightarrow \end{array}} \\
\multicolumn{1}{c}{\begin{array}{lcr} \leftarrow & a_{i} & \rightarrow \end{array}} \\
\end{array}
\right) \neq \left(\begin{array}{c} 
 \multicolumn{1}{c}{\begin{array}{lcr} \leftarrow & b_{1} & \rightarrow \end{array}} \\
\multicolumn{1}{c}{\begin{array}{lcr} \leftarrow & b_{2} & \rightarrow \end{array}} \\
\multicolumn{1}{c}{\begin{array}{lcr} \leftarrow & \vdots & \rightarrow \end{array}} \\
\multicolumn{1}{c}{\begin{array}{lcr} \leftarrow & b_{j} & \rightarrow \end{array}} \\
\end{array}
\right)\right) \textrm{ if } i \in \mathbb{N} ,  j \in \mathbb{N} ,  i \neq j\right..

stored_expr.style_options()

name	description	default	current value	related methods
condition_delimiter	'comma' or 'and'	comma	comma	('with_comma_delimiter', 'with_conjunction_delimiter')

# display the expression information
stored_expr.expr_info()

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