Mixing
How to prove by equational proof
⊢(∃x)A≡(∃z)A[x:=z] where z is fresh for A
rules same as here
I proved via hilbert style to prove
⊢(∀x) A ≡ (∀z) A [x:=z] where z is fresh for A
but struggling with equational proof for
⊢(∃x)A≡(∃z)A[x:=z] where z is fresh for A
logic predicate-logic
edited Nov 21 '18 at 8:03
Mauro ALLEGRANZA
64.4k448112
asked Nov 20 '18 at 18:10
TaeCoda
15
add a comment |
⊢(∃x)A≡(∃z)A[x:=z] where z is fresh for A
rules same as here
I proved via hilbert style to prove
⊢(∀x) A ≡ (∀z) A [x:=z] where z is fresh for A
but struggling with equational proof for
⊢(∃x)A≡(∃z)A[x:=z] where z is fresh for A
logic predicate-logic
edited Nov 21 '18 at 8:03
Mauro ALLEGRANZA
64.4k448112
asked Nov 20 '18 at 18:10
TaeCoda
15
Maybe you have to use the fact/definition : $(∃x)A equiv lnot (∀x) lnot A$.
– Mauro ALLEGRANZA
Nov 21 '18 at 8:02
using that definition, I will get ¬(∀x) ¬A ≡ ¬(∀z) ¬A [x:=z] ? How do you do this equational proof to prove that?
– TaeCoda
Nov 22 '18 at 17:53
add a comment |
⊢(∃x)A≡(∃z)A[x:=z] where z is fresh for A
rules same as here
I proved via hilbert style to prove
⊢(∀x) A ≡ (∀z) A [x:=z] where z is fresh for A
but struggling with equational proof for
⊢(∃x)A≡(∃z)A[x:=z] where z is fresh for A
logic predicate-logic
edited Nov 21 '18 at 8:03
Mauro ALLEGRANZA
64.4k448112
asked Nov 20 '18 at 18:10
TaeCoda
15
⊢(∃x)A≡(∃z)A[x:=z] where z is fresh for A
rules same as here
I proved via hilbert style to prove
⊢(∀x) A ≡ (∀z) A [x:=z] where z is fresh for A
but struggling with equational proof for
⊢(∃x)A≡(∃z)A[x:=z] where z is fresh for A
logic predicate-logic
logic predicate-logic
edited Nov 21 '18 at 8:03
Mauro ALLEGRANZA
64.4k448112
asked Nov 20 '18 at 18:10
TaeCoda
15
edited Nov 21 '18 at 8:03
Mauro ALLEGRANZA
64.4k448112
asked Nov 20 '18 at 18:10
TaeCoda
15
edited Nov 21 '18 at 8:03
Mauro ALLEGRANZA
64.4k448112
edited Nov 21 '18 at 8:03
Mauro ALLEGRANZA
64.4k448112
edited Nov 21 '18 at 8:03
Mauro ALLEGRANZA
64.4k448112
64.4k448112
asked Nov 20 '18 at 18:10
TaeCoda
15
asked Nov 20 '18 at 18:10
TaeCoda
15
asked Nov 20 '18 at 18:10
TaeCoda
15
15
Maybe you have to use the fact/definition : $(∃x)A equiv lnot (∀x) lnot A$.
– Mauro ALLEGRANZA
Nov 21 '18 at 8:02
using that definition, I will get ¬(∀x) ¬A ≡ ¬(∀z) ¬A [x:=z] ? How do you do this equational proof to prove that?
– TaeCoda
Nov 22 '18 at 17:53
add a comment |
Maybe you have to use the fact/definition : $(∃x)A equiv lnot (∀x) lnot A$.
– Mauro ALLEGRANZA
Nov 21 '18 at 8:02
using that definition, I will get ¬(∀x) ¬A ≡ ¬(∀z) ¬A [x:=z] ? How do you do this equational proof to prove that?
– TaeCoda
Nov 22 '18 at 17:53
Maybe you have to use the fact/definition : $(∃x)A equiv lnot (∀x) lnot A$.
– Mauro ALLEGRANZA
Nov 21 '18 at 8:02
Maybe you have to use the fact/definition : $(∃x)A equiv lnot (∀x) lnot A$.
– Mauro ALLEGRANZA
Nov 21 '18 at 8:02
using that definition, I will get ¬(∀x) ¬A ≡ ¬(∀z) ¬A [x:=z] ? How do you do this equational proof to prove that?
– TaeCoda
Nov 22 '18 at 17:53
using that definition, I will get ¬(∀x) ¬A ≡ ¬(∀z) ¬A [x:=z] ? How do you do this equational proof to prove that?
– TaeCoda
Nov 22 '18 at 17:53
add a comment |
0
active
oldest
votes
Your Answer
StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
});
});
}, "mathjax-editing");
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "69"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});
function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3006685%2fhow-to-prove-by-equational-proof%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
0
active
oldest
votes
0
active
oldest
votes
active
oldest
votes
active
oldest
votes
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Some of your past answers have not been well-received, and you're in danger of being blocked from answering.
Please pay close attention to the following guidance:
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3006685%2fhow-to-prove-by-equational-proof%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Maybe you have to use the fact/definition : $(∃x)A equiv lnot (∀x) lnot A$.
– Mauro ALLEGRANZA
Nov 21 '18 at 8:02
using that definition, I will get ¬(∀x) ¬A ≡ ¬(∀z) ¬A [x:=z] ? How do you do this equational proof to prove that?
– TaeCoda
Nov 22 '18 at 17:53