Expression of type Forall

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 Equals, FALSE, Forall
from proveit.numbers import one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = 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))

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())

\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)

stored_expr.style_options()

name	description	default	current value	related methods
with_wrapping	If 'True', wrap the Expression after the parameters	None	None/False	('with_wrapping',)
condition_wrapping	Wrap 'before' or 'after' the condition (or None).	None	None/False	('with_wrap_after_condition', 'with_wrap_before_condition')
wrap_params	If 'True', wraps every two parameters AND wraps the Expression after the parameters	None	None/False	('with_params',)
justification	justify to the 'left', 'center', or 'right' in the array cells	center	center	('with_justification',)

# display the expression information
stored_expr.expr_info()

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