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Revising for Wednesday's lecture

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This commit is contained in:
Adam Chlipala 2022-02-06 13:03:43 -05:00
parent bec1b1b919
commit 65b817d7ae
1 changed files with 6 additions and 0 deletions
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6
RuleInduction.v
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@ -19,6 +19,8 @@ Theorem favorites_below_50 : forall n, my_favorite_numbers n -> n < 50.
Proof. Proof.
simplify. simplify.
invert H. invert H.
(* [invert]: case analysis on which rules may have been used to prove an
* instance of an inductive predicate *)
linear_arithmetic. linear_arithmetic.
linear_arithmetic. linear_arithmetic.
linear_arithmetic. linear_arithmetic.
@ -82,6 +84,8 @@ Theorem lt_lt' : forall n m, n < m -> lt' n m.
Proof. Proof.
simplify. simplify.
replace m with (S (m - n - 1) + n) by linear_arithmetic. replace m with (S (m - n - 1) + n) by linear_arithmetic.
(* [replace]: change a subterm into another one, adding an obligation to prove
* equality of the two. *)
apply lt_lt''. apply lt_lt''.
Qed. Qed.
@ -260,6 +264,8 @@ Module SimplePropositional.
apply ValidTruth. apply ValidTruth.
propositional. propositional.
(* [propositional]: simplify goal according to the rules of propositional
* logic, a decidable theory. *)
propositional. propositional.
apply ValidAnd. apply ValidAnd.