Expression of type Implies

from the theory of proveit.logic.booleans

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, PofA
from proveit.logic import And, Boolean, Forall, Implies, PofFalse, PofTrue

# build up the expression from sub-expressions
expr = Implies(Forall(instance_param_or_params = [A], instance_expr = PofA, domain = Boolean), And(PofTrue, PofFalse))

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 \in \mathbb{B}}~P\left(A\right)\right] \Rightarrow \left(P\left(\top\right) \land P\left(\bot\right)\right)

stored_expr.style_options()

name	description	default	current value	related methods
operation	'infix' or 'function' style formatting	infix	infix
wrap_positions	position(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.	()	()	('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	center	center	('with_justification',)
direction	Direction of the relation (normal or reversed)	normal	normal	('with_direction_reversed', 'is_reversed')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 1 operands: 2
1	Literal
2	ExprTuple	3, 4
3	Operation	operator: 5 operand: 9
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	9
7	Literal
8	ExprTuple	10, 11
9	Lambda	parameter: 23 body: 12
10	Operation	operator: 19 operand: 17
11	Operation	operator: 19 operand: 18
12	Conditional	value: 15 condition: 16
13	ExprTuple	17
14	ExprTuple	18
15	Operation	operator: 19 operand: 23
16	Operation	operator: 21 operands: 22
17	Literal
18	Literal
19	Variable
20	ExprTuple	23
21	Literal
22	ExprTuple	23, 24
23	Variable
24	Literal