Equivalence between apply and Isar styles in Isabelle
up vote
1
down vote
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Are apply style and Isar-proofs equivalents? This is a question that I have thougth for some time. Of course, Isar-proofs are much more readable, maintanable and easy to write (?) but my question is whether you could prove exactly the same things with both styles.
As an example, I'm currently working on a proof where I need to leave:
apply(simp split: prod.splits)
using some_lemma by fastforce
What is the equivalent form of these commands in apply and Isar style? Actually, I'm more interested in the Isar style since I'm told that it is bad style to mix styles.
isabelle
asked Nov 9 at 23:03
Javier
645723
add a comment |
up vote
1
down vote
favorite
Are apply style and Isar-proofs equivalents? This is a question that I have thougth for some time. Of course, Isar-proofs are much more readable, maintanable and easy to write (?) but my question is whether you could prove exactly the same things with both styles.
As an example, I'm currently working on a proof where I need to leave:
apply(simp split: prod.splits)
using some_lemma by fastforce
What is the equivalent form of these commands in apply and Isar style? Actually, I'm more interested in the Isar style since I'm told that it is bad style to mix styles.
isabelle
asked Nov 9 at 23:03
Javier
645723
add a comment |
up vote
1
down vote
favorite
up vote
1
down vote
favorite
Are apply style and Isar-proofs equivalents? This is a question that I have thougth for some time. Of course, Isar-proofs are much more readable, maintanable and easy to write (?) but my question is whether you could prove exactly the same things with both styles.
As an example, I'm currently working on a proof where I need to leave:
apply(simp split: prod.splits)
using some_lemma by fastforce
What is the equivalent form of these commands in apply and Isar style? Actually, I'm more interested in the Isar style since I'm told that it is bad style to mix styles.
isabelle
asked Nov 9 at 23:03
Javier
645723
Are apply style and Isar-proofs equivalents? This is a question that I have thougth for some time. Of course, Isar-proofs are much more readable, maintanable and easy to write (?) but my question is whether you could prove exactly the same things with both styles.
As an example, I'm currently working on a proof where I need to leave:
apply(simp split: prod.splits)
using some_lemma by fastforce
What is the equivalent form of these commands in apply and Isar style? Actually, I'm more interested in the Isar style since I'm told that it is bad style to mix styles.
isabelle
isabelle
asked Nov 9 at 23:03
Javier
645723
asked Nov 9 at 23:03
Javier
645723
asked Nov 9 at 23:03
Javier
645723
asked Nov 9 at 23:03
Javier
645723
asked Nov 9 at 23:03
Javier
645723
645723
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
up vote
2
down vote
accepted
The equivalent Isar style would be:
have "P"
using some_lemma by fastforce
then have "Q"
by (simp split: prod.splits)
Where "P" is represents the intermediate goal state after the first apply.
In general, anything provable can be proved both in Isar and in apply style; both have their strengths and weaknesses.
I personally use the style where I try to structure my proofs outside-in: outside (like induction) Isar, and if necessary, inside (like simplification, low-level stuff) with apply.
In general though I recommend you stay within Isar as much as possible.
answered Nov 9 at 23:24
larsrh
2,014321
what if "P" is a huge subgoal? would you paste it as it is?
– Javier
Nov 14 at 18:43
in that case, for me writing using some_lemma by (simp split: prod.splits) (fastforce) works
– Javier
Nov 14 at 18:47
@Javier That's always a trade-off. Often, the proof can be restructured to avoid huge intermediate statements. Other times, it can't.
– larsrh
Nov 15 at 20:05
add a comment |
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
2
down vote
accepted
The equivalent Isar style would be:
have "P"
using some_lemma by fastforce
then have "Q"
by (simp split: prod.splits)
Where "P" is represents the intermediate goal state after the first apply.
In general, anything provable can be proved both in Isar and in apply style; both have their strengths and weaknesses.
I personally use the style where I try to structure my proofs outside-in: outside (like induction) Isar, and if necessary, inside (like simplification, low-level stuff) with apply.
In general though I recommend you stay within Isar as much as possible.
answered Nov 9 at 23:24
larsrh
2,014321
what if "P" is a huge subgoal? would you paste it as it is?
– Javier
Nov 14 at 18:43
in that case, for me writing using some_lemma by (simp split: prod.splits) (fastforce) works
– Javier
Nov 14 at 18:47
@Javier That's always a trade-off. Often, the proof can be restructured to avoid huge intermediate statements. Other times, it can't.
– larsrh
Nov 15 at 20:05
add a comment |
up vote
2
down vote
accepted
The equivalent Isar style would be:
have "P"
using some_lemma by fastforce
then have "Q"
by (simp split: prod.splits)
Where "P" is represents the intermediate goal state after the first apply.
In general, anything provable can be proved both in Isar and in apply style; both have their strengths and weaknesses.
I personally use the style where I try to structure my proofs outside-in: outside (like induction) Isar, and if necessary, inside (like simplification, low-level stuff) with apply.
In general though I recommend you stay within Isar as much as possible.
answered Nov 9 at 23:24
larsrh
2,014321
what if "P" is a huge subgoal? would you paste it as it is?
– Javier
Nov 14 at 18:43
in that case, for me writing using some_lemma by (simp split: prod.splits) (fastforce) works
– Javier
Nov 14 at 18:47
@Javier That's always a trade-off. Often, the proof can be restructured to avoid huge intermediate statements. Other times, it can't.
– larsrh
Nov 15 at 20:05
add a comment |
up vote
2
down vote
accepted
up vote
2
down vote
accepted
The equivalent Isar style would be:
have "P"
using some_lemma by fastforce
then have "Q"
by (simp split: prod.splits)
Where "P" is represents the intermediate goal state after the first apply.
In general, anything provable can be proved both in Isar and in apply style; both have their strengths and weaknesses.
I personally use the style where I try to structure my proofs outside-in: outside (like induction) Isar, and if necessary, inside (like simplification, low-level stuff) with apply.
In general though I recommend you stay within Isar as much as possible.
answered Nov 9 at 23:24
larsrh
2,014321
The equivalent Isar style would be:
have "P"
using some_lemma by fastforce
then have "Q"
by (simp split: prod.splits)
Where "P" is represents the intermediate goal state after the first apply.
In general, anything provable can be proved both in Isar and in apply style; both have their strengths and weaknesses.
I personally use the style where I try to structure my proofs outside-in: outside (like induction) Isar, and if necessary, inside (like simplification, low-level stuff) with apply.
In general though I recommend you stay within Isar as much as possible.
answered Nov 9 at 23:24
larsrh
2,014321
answered Nov 9 at 23:24
larsrh
2,014321
answered Nov 9 at 23:24
larsrh
2,014321
answered Nov 9 at 23:24
larsrh
2,014321
2,014321
what if "P" is a huge subgoal? would you paste it as it is?
– Javier
Nov 14 at 18:43
in that case, for me writing using some_lemma by (simp split: prod.splits) (fastforce) works
– Javier
Nov 14 at 18:47
@Javier That's always a trade-off. Often, the proof can be restructured to avoid huge intermediate statements. Other times, it can't.
– larsrh
Nov 15 at 20:05
add a comment |
what if "P" is a huge subgoal? would you paste it as it is?
– Javier
Nov 14 at 18:43
in that case, for me writing using some_lemma by (simp split: prod.splits) (fastforce) works
– Javier
Nov 14 at 18:47
@Javier That's always a trade-off. Often, the proof can be restructured to avoid huge intermediate statements. Other times, it can't.
– larsrh
Nov 15 at 20:05
what if "P" is a huge subgoal? would you paste it as it is?
– Javier
Nov 14 at 18:43
what if "P" is a huge subgoal? would you paste it as it is?
– Javier
Nov 14 at 18:43
in that case, for me writing using some_lemma by (simp split: prod.splits) (fastforce) works
– Javier
Nov 14 at 18:47
in that case, for me writing using some_lemma by (simp split: prod.splits) (fastforce) works
– Javier
Nov 14 at 18:47
@Javier That's always a trade-off. Often, the proof can be restructured to avoid huge intermediate statements. Other times, it can't.
– larsrh
Nov 15 at 20:05
@Javier That's always a trade-off. Often, the proof can be restructured to avoid huge intermediate statements. Other times, it can't.
– larsrh
Nov 15 at 20:05
add a comment |
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