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Proof step 44 from proof replayorphans-prepost (previous step)

(inodekey(ino) ∈ ks0 ⊃ (∅)[datakey(ino, n)];ri0[datakey(ino, n)]) = (datakey(ino, n) ∈ ri1 ∧ inodekey(ino) ∈ ro1 ⊃ (∅)[datakey(ino, n)];ri1[datakey(ino, n)]), ¬ inodekey(ino) ∈ ks0 ↔ datakey(ino, n) ∈ ri1 ∧ ¬ inodekey(ino) ∈ ro1, ro1.inodes?, ks0.inodes?, datakey(ino, n) ∈ ri0, key ∈ ks0, key ∈ ro1, ks0 ⊆ ro1, ∀ key1. (key1 ∈ ri0 ∧ ¬ key1 ∈ ks0 ∧ (¬ key1.data? ∨ ¬ inodekey(key1.ino) ∈ ks0) ↔ key1 ∈ ri1 ∧ ¬ key1 ∈ ro1 ∧ (¬ key1.data? ∨ ¬ inodekey(key1.ino) ∈ ro1)) ∧ (key1 ∈ ri0 ∧ key1.data? ∧ inodekey(key1.ino) ∈ ks0 ⊃ (∅)[key1];(key1 ∈ ks0 ⊃ (∅)[key1];ri0[key1])) = (key1 ∈ ri1 ∧ key1.data? ∧ inodekey(key1.ino) ∈ ro1 ⊃ (∅)[key1];(key1 ∈ ro1 ⊃ (∅)[key1];ri1[key1])) ⊦ # ks0 = 0, # ro1 = 0, (key = datakey(ino, n) ⊃ (∅)[datakey(ino, n)] ;((¬ key.inode? ∨ ino ≠ key.ino) ∧ inodekey(ino) ∈ ks0 ⊃ (∅)[datakey(ino, n)];(ino = key.ino ⊃ (∅)[datakey(key.ino, n)];ri0[datakey(ino, n)])) ) = (inodekey(ino) ∈ ks0 ⊃ (∅)[datakey(ino, n)];ri0[datakey(ino, n)]), ks0 = ∅, ro1 = ∅

Heuristic nonsplitting cut applied rule cut formula

And obtained the following new goals

Proof step 45:
(inodekey(ino) ∈ ks0 ⊃ (∅)[datakey(ino, n)];ri0[datakey(ino, n)]) = (datakey(ino, n) ∈ ri1 ∧ inodekey(ino) ∈ ro1 ⊃ (∅)[datakey(ino, n)];ri1[datakey(ino, n)]), ¬ inodekey(ino) ∈ ks0 ↔ datakey(ino, n) ∈ ri1 ∧ ¬ inodekey(ino) ∈ ro1, ks0.inodes?, ro1.inodes?, key ∈ ro1, key ∈ ks0, datakey(ino, n) ∈ ri0, ks0 ⊆ ro1, ∀ key1. (key1 ∈ ri0 ∧ ¬ key1 ∈ ks0 ∧ (¬ key1.data? ∨ ¬ inodekey(key1.ino) ∈ ks0) ↔ key1 ∈ ri1 ∧ ¬ key1 ∈ ro1 ∧ (¬ key1.data? ∨ ¬ inodekey(key1.ino) ∈ ro1)) ∧ (key1 ∈ ri0 ∧ key1.data? ∧ inodekey(key1.ino) ∈ ks0 ⊃ (∅)[key1];(key1 ∈ ks0 ⊃ (∅)[key1];ri0[key1])) = (key1 ∈ ri1 ∧ key1.data? ∧ inodekey(key1.ino) ∈ ro1 ⊃ (∅)[key1];(key1 ∈ ro1 ⊃ (∅)[key1];ri1[key1])) ⊦ # ro1 = 0, # ks0 = 0, (key = datakey(ino, n) ⊃ (∅)[datakey(ino, n)] ;((¬ key.inode? ∨ ino ≠ key.ino) ∧ inodekey(ino) ∈ ks0 ⊃ (∅)[datakey(ino, n)];(ino = key.ino ⊃ (∅)[datakey(key.ino, n)];ri0[datakey(ino, n)])) ) = (inodekey(ino) ∈ ks0 ⊃ (∅)[datakey(ino, n)];ri0[datakey(ino, n)]), key = datakey(ino, n), ks0 = ∅, ro1 = ∅

Rule argument

fma: key = datakey(ino, n)

Additional information

Used simplifier rules: ⊦ ks.inodes? → ¬ datakey(ino, n) ∈ ks; (s) Used formulas: key = datakey(ino, n)