Expression of type Conditional

from the theory of proveit.core_expr_types.conditionals

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, ConditionalSet, ExprRange, IndexedVar, Variable, a, b, c, m, n
from proveit.core_expr_types import a_1_to_m, c_1_to_n
from proveit.logic import And, Equals, FALSE, Forall, InSet
from proveit.numbers import Natural, one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Conditional(Forall(instance_param_or_params = [a_1_to_m, b, c_1_to_n], instance_expr = Equals(ConditionalSet(ExprRange(sub_expr1, Conditional(IndexedVar(a, sub_expr1), FALSE), one, m), b, ExprRange(sub_expr1, Conditional(IndexedVar(c, sub_expr1), FALSE), one, n)), b)), And(InSet(m, Natural), InSet(n, 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\{\forall_{a_{1}, a_{2}, \ldots, a_{m}, b, c_{1}, c_{2}, \ldots, c_{n}}~\left(\left\{\begin{array}{ccc}a_{1} \textrm{ if } \bot \\ a_{2} \textrm{ if } \bot \\  \vdots \\ a_{m} \textrm{ if } \bot \\ b \\ c_{1} \textrm{ if } \bot \\ c_{2} \textrm{ if } \bot \\  \vdots \\ c_{n} \textrm{ if } \bot\end{array}\right.. = b\right) \textrm{ if } m \in \mathbb{N} ,  n \in \mathbb{N}\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
7	Lambda	parameters: 10 body: 11
8	Operation	operator: 13 operands: 12
9	Operation	operator: 13 operands: 14
10	ExprTuple	15, 26, 16
11	Operation	operator: 17 operands: 18
12	ExprTuple	29, 19
13	Literal
14	ExprTuple	32, 19
15	ExprRange	lambda_map: 20 start_index: 31 end_index: 29
16	ExprRange	lambda_map: 21 start_index: 31 end_index: 32
17	Literal
18	ExprTuple	22, 26
19	Literal
20	Lambda	parameter: 41 body: 35
21	Lambda	parameter: 41 body: 36
22	Operation	operator: 23 operands: 24
23	Literal
24	ExprTuple	25, 26, 27
25	ExprRange	lambda_map: 28 start_index: 31 end_index: 29
26	Variable
27	ExprRange	lambda_map: 30 start_index: 31 end_index: 32
28	Lambda	parameter: 41 body: 33
29	Variable
30	Lambda	parameter: 41 body: 34
31	Literal
32	Variable
33	Conditional	value: 35 condition: 37
34	Conditional	value: 36 condition: 37
35	IndexedVar	variable: 38 index: 41
36	IndexedVar	variable: 39 index: 41
37	Literal
38	Variable
39	Variable
40	ExprTuple	41
41	Variable