Expression of type Lambda

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, Lambda, 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 = Lambda([i, j], 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(i, j\right) \mapsto \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()

no style options

# display the expression information
stored_expr.expr_info()

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