59 lines
1.9 KiB
Text
59 lines
1.9 KiB
Text
simplification rules for iff
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#1, ?x_0 ↔ ?x_0 ↦ true
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#1, false ↔ ?x_0 ↦ ¬?x_0
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#1, ?x_0 ↔ false ↦ ¬?x_0
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#1, true ↔ ?x_0 ↦ ?x_0
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#1, ?x_0 ↔ true ↦ ?x_0
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#0, false ↔ true ↦ false
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#0, true ↔ false ↦ false
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#1, ¬?x_0 ↔ ?x_0 ↦ false
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#1, ?x_0 ↔ ¬?x_0 ↦ false
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#2, ?x_0 - ?x_1 ≤ ?x_0 ↦ true
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#1, 0 ≤ ?x_0 ↦ true
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#1, succ ?x_0 ≤ ?x_0 ↦ false
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#1, pred ?x_0 ≤ ?x_0 ↦ true
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#1, ?x_0 ≤ succ ?x_0 ↦ true
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#1, ?x_0 ∧ ?x_0 ↦ ?x_0
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#1, ?x_0 ∧ ¬?x_0 ↦ false
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#1, ¬?x_0 ∧ ?x_0 ↦ false
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#1, false ∧ ?x_0 ↦ false
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#1, ?x_0 ∧ false ↦ false
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#1, true ∧ ?x_0 ↦ ?x_0
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#1, ?x_0 ∧ true ↦ ?x_0
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#3 perm, ?x_0 ∧ ?x_1 ∧ ?x_2 ↦ ?x_1 ∧ ?x_0 ∧ ?x_2
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#3, (?x_0 ∧ ?x_1) ∧ ?x_2 ↦ ?x_0 ∧ ?x_1 ∧ ?x_2
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#2 perm, ?x_0 ∧ ?x_1 ↦ ?x_1 ∧ ?x_0
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#2, ?x_1 == ?x_1 ↦ true
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#2, ?x_0 - ?x_1 < succ ?x_0 ↦ true
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#1, ?x_0 < 0 ↦ false
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#1, ?x_0 < succ ?x_0 ↦ true
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#1, 0 < succ ?x_0 ↦ true
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#1, ?x_0 ∨ ?x_0 ↦ ?x_0
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#1, false ∨ ?x_0 ↦ ?x_0
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#1, ?x_0 ∨ false ↦ ?x_0
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#1, true ∨ ?x_0 ↦ true
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#1, ?x_0 ∨ true ↦ true
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#3 perm, ?x_0 ∨ ?x_1 ∨ ?x_2 ↦ ?x_1 ∨ ?x_0 ∨ ?x_2
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#3, (?x_0 ∨ ?x_1) ∨ ?x_2 ↦ ?x_0 ∨ ?x_1 ∨ ?x_2
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#2 perm, ?x_0 ∨ ?x_1 ↦ ?x_1 ∨ ?x_0
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#2, ?x_1 = ?x_1 ↦ true
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#4, ite ?x_0 ?x_1 ?x_2 ↦ (?x_0 → ?x_1) ∧ (¬?x_0 → ?x_2)
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#0, ¬true ↦ false
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#2, ¬?x_1 = ?x_1 ↦ false
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#0, ¬false ↦ true
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#1, false → ?x_0 ↦ true
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#1, true → ?x_0 ↦ ?x_0
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#1, ?x_0 → true ↦ true
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#1, ?x_0 → ?x_0 ↦ true
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#3, ?x_0 → ?x_1 ∧ ?x_2 ↦ (?x_0 → ?x_1) ∧ (?x_0 → ?x_2)
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#3, ?x_0 ∨ ?x_1 → ?x_2 ↦ (?x_0 → ?x_2) ∧ (?x_1 → ?x_2)
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#3, ?x_0 ∧ ?x_1 → ?x_2 ↦ ?x_0 → ?x_1 → ?x_2
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simplification rules for eq
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#1, g ?x_0 ↦ f ?x_0 + 1
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#2, g ?x_0 ↦ 1
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#2, f ?x_0 ↦ 0
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#3, ite false ?x_1 ?x_2 ↦ ?x_2
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#3, ite true ?x_1 ?x_2 ↦ ?x_1
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#4, ite ?x_0 ?x_3 ?x_3 ↦ ?x_3
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#1, 0 - ?x_0 ↦ 0
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#2, succ ?x_0 - succ ?x_1 ↦ ?x_0 - ?x_1
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