Expression of type Forall

from the theory of proveit.logic.booleans.disjunction

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 A, C, ExprRange, IndexedVar, Variable, m
from proveit.core_expr_types import A_1_to_m
from proveit.logic import Boolean, Forall, Implies, Or
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], instance_expr = Forall(instance_param_or_params = [C], instance_expr = C, condition = ExprRange(sub_expr1, Implies(IndexedVar(A, sub_expr1), C), one, m)), domain = Boolean, condition = Or(A_1_to_m))

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} \in \mathbb{B}~|~A_{1} \lor  A_{2} \lor  \ldots \lor  A_{m}}~\left[\forall_{C~|~\left(A_{1} \Rightarrow C\right), \left(A_{2} \Rightarrow C\right), \ldots, \left(A_{m} \Rightarrow C\right)}~C\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: 6 operand: 2
1	ExprTuple	2
2	Lambda	parameters: 16 body: 3
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operand: 9
5	Operation	operator: 20 operands: 8
6	Literal
7	ExprTuple	9
8	ExprTuple	10, 11
9	Lambda	parameter: 34 body: 13
10	ExprRange	lambda_map: 14 start_index: 28 end_index: 29
11	Operation	operator: 15 operands: 16
12	ExprTuple	34
13	Conditional	value: 34 condition: 17
14	Lambda	parameter: 37 body: 18
15	Literal
16	ExprTuple	19
17	Operation	operator: 20 operands: 21
18	Operation	operator: 22 operands: 23
19	ExprRange	lambda_map: 24 start_index: 28 end_index: 29
20	Literal
21	ExprTuple	25
22	Literal
23	ExprTuple	33, 26
24	Lambda	parameter: 37 body: 33
25	ExprRange	lambda_map: 27 start_index: 28 end_index: 29
26	Literal
27	Lambda	parameter: 37 body: 30
28	Literal
29	Variable
30	Operation	operator: 31 operands: 32
31	Literal
32	ExprTuple	33, 34
33	IndexedVar	variable: 35 index: 37
34	Variable
35	Variable
36	ExprTuple	37
37	Variable