Expression of type Implies

from the theory of proveit.logic.sets.functions.bijections

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, B, C, Conditional, Function, Lambda, f, fx, g, x
from proveit.logic import And, Bijections, Implies, InSet

# build up the expression from sub-expressions
expr = Implies(And(InSet(f, Bijections(A, B)), InSet(g, Bijections(B, C))), InSet(Lambda(x, Conditional(Function(g, [fx]), InSet(x, A))), Bijections(A, C))).with_wrapping_at(1)

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())

\begin{array}{c} \begin{array}{l} \left(\left(f \in \left[A \xrightarrow[\text{onto}]{\text{1-to-1}} B\right]\right) \land \left(g \in \left[B \xrightarrow[\text{onto}]{\text{1-to-1}} C\right]\right)\right) \\  \Rightarrow \left(\left[x \mapsto \left\{g\left(f\left(x\right)\right) \textrm{ if } x \in A\right..\right] \in \left[A \xrightarrow[\text{onto}]{\text{1-to-1}} C\right]\right) \end{array} \end{array}

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.	()	(1)	('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 operands: 6
4	Operation	operator: 25 operands: 7
5	Literal
6	ExprTuple	8, 9
7	ExprTuple	10, 11
8	Operation	operator: 25 operands: 12
9	Operation	operator: 25 operands: 13
10	Lambda	parameter: 33 body: 14
11	Operation	operator: 21 operands: 15
12	ExprTuple	31, 16
13	ExprTuple	23, 17
14	Conditional	value: 18 condition: 19
15	ExprTuple	30, 28
16	Operation	operator: 21 operands: 20
17	Operation	operator: 21 operands: 22
18	Operation	operator: 23 operand: 29
19	Operation	operator: 25 operands: 26
20	ExprTuple	30, 27
21	Literal
22	ExprTuple	27, 28
23	Variable
24	ExprTuple	29
25	Literal
26	ExprTuple	33, 30
27	Variable
28	Variable
29	Operation	operator: 31 operand: 33
30	Variable
31	Variable
32	ExprTuple	33
33	Variable