7 lines
583 B
Text
7 lines
583 B
Text
Formula.count_quantifiers._eq_1 : ∀ (x : Nat) (f₁ f₂ : Formula x),
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Formula.count_quantifiers (Formula.imp f₁ f₂) = Formula.count_quantifiers f₁ + Formula.count_quantifiers f₂
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Formula.count_quantifiers._eq_2 : ∀ (x : Nat) (f : Formula (x + 1)),
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Formula.count_quantifiers (Formula.all f) = Formula.count_quantifiers f + 1
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Formula.count_quantifiers._eq_3 : ∀ (x : Nat) (x_1 : Formula x),
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(∀ (f₁ f₂ : Formula x), x_1 = Formula.imp f₁ f₂ → False) →
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(∀ (f : Formula (x + 1)), x_1 = Formula.all f → False) → Formula.count_quantifiers x_1 = 0
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