64688d4cee
The induction principle used by `induction` may have explicit parameters that are not motive, target or “real” alternatives (that have the `motive` as conclusion), e.g. restrictions on the `motive` or other parameters. Previously, `induction` would treat them as normal alternatives, and try to re-introduce the automatically reverted hypotheses. But this only works when the `motive` is actually the conclusion in the type of that alternative. We now pay attention to that, thread that information through, and only revert when needed. Fixes #3212.
60 lines
1.9 KiB
Text
60 lines
1.9 KiB
Text
namespace SillyParam
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set_option linter.unusedVariables false in
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theorem nat_rec_with_string (some_param : String) {motive : Nat → Prop}
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(zero : motive .zero) (succ : ∀ n, motive n → motive (.succ n)) : ∀ n, motive n :=
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@Nat.rec motive zero succ
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example (n m : Nat) (h : n ≠ zero) : Nat.add m n ≠ zero := by
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induction n using nat_rec_with_string
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case some_param =>
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show String
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exact "heh"
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case zero => sorry
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case succ => sorry
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end SillyParam
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namespace RestrictedMotive
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axiom Restriction : (Nat → Prop) → Prop
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axiom restricted_induction {motive : Nat → Prop} (h : Restriction motive)
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(zero : motive .zero) (succ : ∀ n, motive n → motive (.succ n)) : ∀ n, motive n
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example (n m : Nat) (h : n ≠ zero) : Nat.add m n ≠ zero := by
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induction n using restricted_induction
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case h =>
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show Restriction _
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sorry
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case zero => sorry
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case succ => sorry
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end RestrictedMotive
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namespace DownInduction
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axiom down_induction {motive : Nat → Prop} (u : Nat) (x : Nat)
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(le_u : x ≤ u) (start : motive u) (step : ∀ x, x < u → motive (x + 1) → motive x) : motive x
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example (n m : Nat) (h : m * m < 100) (h2 : n ≤ m) : n * n < 100 := by
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induction n using down_induction
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case u => exact m -- (could have used `using down_induction (u := m)` of course)
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case le_u =>
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-- This does not work as hoped for yet: `induction` will revert `h2`, because it mentions `n`,
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-- but we’d like to keep it outside of the motive here.
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sorry
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case start => exact h
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case step x hlt IH =>
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have IH := IH hlt
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sorry
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-- Unfortunately, this doesn’t work either:
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-- example (n m : Nat) (h : m * m < 100) (h2 : n ≤ m) : n * n < 100 := by
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-- induction n using down_induction (le_u := h2)
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-- because after this, the target `n` is no longer a universally qualified variable
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--
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-- This probably could be made to work with a bit more refactoring.
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end DownInduction
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