Expression of type Forall

from the theory of proveit.logic.booleans.conjunction

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.core_expr_types import A_1_to_l, B_1_to_m, C_1_to_n
from proveit.logic import And, Forall

# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [A_1_to_l, B_1_to_m, C_1_to_n], instance_expr = And(A_1_to_l, And(B_1_to_m), C_1_to_n), condition = And(A_1_to_l, B_1_to_m, C_1_to_n))

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_{l}, B_{1}, B_{2}, \ldots, B_{m}, C_{1}, C_{2}, \ldots, C_{n}~|~A_{1}, A_{2}, \ldots, A_{l},B_{1}, B_{2}, \ldots, B_{m},C_{1}, C_{2}, \ldots, C_{n}}~\left(A_{1} \land  A_{2} \land  \ldots \land  A_{l} \land \left(B_{1} \land  B_{2} \land  \ldots \land  B_{m}\right)\land C_{1} \land  C_{2} \land  \ldots \land  C_{n}\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: 8 body: 4
4	Conditional	value: 5 condition: 6
5	Operation	operator: 12 operands: 7
6	Operation	operator: 12 operands: 8
7	ExprTuple	10, 9, 11
8	ExprTuple	10, 18, 11
9	Operation	operator: 12 operands: 13
10	ExprRange	lambda_map: 14 start_index: 22 end_index: 15
11	ExprRange	lambda_map: 16 start_index: 22 end_index: 17
12	Literal
13	ExprTuple	18
14	Lambda	parameter: 29 body: 19
15	Variable
16	Lambda	parameter: 29 body: 20
17	Variable
18	ExprRange	lambda_map: 21 start_index: 22 end_index: 23
19	IndexedVar	variable: 24 index: 29
20	IndexedVar	variable: 25 index: 29
21	Lambda	parameter: 29 body: 26
22	Literal
23	Variable
24	Variable
25	Variable
26	IndexedVar	variable: 27 index: 29
27	Variable
28	ExprTuple	29
29	Variable