Mathbox for Jarvin Udandy |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > mdandysum2p2e4 | Structured version Visualization version Unicode version |
Description: CONTRADICTION PROVED AT 1
+ 1 = 2 . Luckily Mario Carneiro did a
successful version of his own.
See Mario's Relevant Work: 1.3.14 Half adder and full adder in propositional calculus. Given the right hypotheses we can prove a dandysum of 2+2=4. The qed step is the value '4' in Decimal BEING IMPLIED by the hypotheses. Note: Values that when added which exceed a 4bit value are not supported. Note: Digits begin from left (least) to right (greatest). e.g. 1000 would be '1', 0100 would be '2'. 0010 would be '4'. How to perceive the hypotheses' bits in order: ( th <-> F. ), ( ta <-> F. ) Would be input value X's first bit, and input value Y's first bit. ( et <-> F. ), ( ze <-> F. ) would be input value X's second bit, and input value Y's second bit. In mdandysum2p2e4, one might imagine what jth or jta could be then do the math with their truths. Also limited to the restriction jth, jta are having opposite truths equivalent to the stated truth constants. (Contributed by Jarvin Udandy, 6-Sep-2016.) |
Ref | Expression |
---|---|
mdandysum2p2e4.1 | jth |
mdandysum2p2e4.2 | jta |
mdandysum2p2e4.a | |
mdandysum2p2e4.b | |
mdandysum2p2e4.c | |
mdandysum2p2e4.d | jth |
mdandysum2p2e4.e | jth |
mdandysum2p2e4.f | jta |
mdandysum2p2e4.g | jta |
mdandysum2p2e4.h | jth |
mdandysum2p2e4.i | jth |
mdandysum2p2e4.j | jth |
mdandysum2p2e4.k | jth |
mdandysum2p2e4.l | |
mdandysum2p2e4.m | jph |
mdandysum2p2e4.n | jps |
mdandysum2p2e4.o | jch |
Ref | Expression |
---|---|
mdandysum2p2e4 | jph jps jch jph jps jch |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | mdandysum2p2e4.a | . 2 | |
2 | mdandysum2p2e4.b | . 2 | |
3 | mdandysum2p2e4.c | . 2 | |
4 | mdandysum2p2e4.d | . . 3 jth | |
5 | mdandysum2p2e4.1 | . . 3 jth | |
6 | 4, 5 | aisbbisfaisf 41069 | . 2 |
7 | mdandysum2p2e4.e | . . 3 jth | |
8 | 7, 5 | aisbbisfaisf 41069 | . 2 |
9 | mdandysum2p2e4.f | . . 3 jta | |
10 | mdandysum2p2e4.2 | . . 3 jta | |
11 | 9, 10 | aiffbbtat 41068 | . 2 |
12 | mdandysum2p2e4.g | . . 3 jta | |
13 | 12, 10 | aiffbbtat 41068 | . 2 |
14 | mdandysum2p2e4.h | . . 3 jth | |
15 | 14, 5 | aisbbisfaisf 41069 | . 2 |
16 | mdandysum2p2e4.i | . . 3 jth | |
17 | 16, 5 | aisbbisfaisf 41069 | . 2 |
18 | mdandysum2p2e4.j | . . 3 jth | |
19 | 18, 5 | aisbbisfaisf 41069 | . 2 |
20 | mdandysum2p2e4.k | . . 3 jth | |
21 | 20, 5 | aisbbisfaisf 41069 | . 2 |
22 | mdandysum2p2e4.l | . 2 | |
23 | mdandysum2p2e4.m | . 2 jph | |
24 | mdandysum2p2e4.n | . 2 jps | |
25 | mdandysum2p2e4.o | . 2 jch | |
26 | 1, 2, 3, 6, 8, 11, 13, 15, 17, 19, 21, 22, 23, 24, 25 | dandysum2p2e4 41165 | 1 jph jps jch jph jps jch |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 196 wo 383 wa 384 wxo 1464 wtru 1484 wfal 1488 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-xor 1465 df-tru 1486 df-fal 1489 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |