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add some rep property #30

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Jan 31, 2024
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add some rep property #30

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3 changes: 3 additions & 0 deletions library/Automata.v
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Original file line number Diff line number Diff line change
Expand Up @@ -24,7 +24,9 @@ Suggest goal default apply rep_len with label Trivial;
Todo rep_add_1: ∀ s, ∀ n, n ≥ 0 → rep s (n + 1) = rep s n + s;

Todo rep_nth: ∀ d: char, ∀ s, ∀ k, k > 0 -> ∀ i, 0 ≤ i ∧ i < k * |s| -> nth d (rep s k) i = nth d s (i mod |s|);
Todo rep_append: ∀ s, ∀ n m, 0 ≤ n → 0 ≤ m → rep s (n + m) = rep s n + rep s m;
Todo valid_paren_n: ∀ n: ℤ, 0 ≤ n → valid_paren (rep "(" n + rep ")" n);
Todo rep_to_repeat: ∀ c: char, ∀ n: ℤ, 0 ≤ n → rep ([c]) n = repeat n c;

Axiom in_Lmult_unfold: ∀ L1 L2: set (list char), ∀ s: list char, s ∈ L1 * L2 → ∃ a b: list char, s = a + b ∧ a ∈ L1 ∧ b ∈ L2;
Axiom in_Lmult_fold: ∀ L1 L2: set (list char), ∀ a b: list char, a ∈ L1 -> b ∈ L2 -> a + b ∈ L1 * L2;
Expand Down Expand Up @@ -196,6 +198,7 @@ Suggest hyp default apply is_decidable_unfold in $n with label Destruct;
Axiom #2 computable: ∀ X Y: U, (X → Y) → U;
Axiom computable_concat: computable (plus (list char));
Axiom computable_const: ∀ X Y: U, ∀ a: Y, computable (λ x: X, a);
Suggest goal default apply computable_const with label Trivial;

Axiom computable_partials_first: ∀ X Y Z: U, ∀ f: (X → Y → Z), ∀ g: (X → Y),
computable f -> computable g -> computable (λ x, f x (g x));
Expand Down
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