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Proof step 31 from proof replayorphans-prepost (previous step)

(key0 ∈ ri0 ∧ key0.data? ∧ inodekey(key0.ino) ∈ ks0 ⊃ (∅)[key0];(key0 ∈ ks0 ⊃ (∅)[key0];ri0[key0])) = (ri1 ⊖ ro1)[key0], key0 ∈ ri0 ∧ ¬ key0 ∈ ks0 ∧ (¬ key0.data? ∨ ¬ inodekey(key0.ino) ∈ ks0) ↔ key0 ∈ ri1 ⊖ ro1, ro1.inodes?, ks0.inodes?, key ∈ ks0, key ∈ ro1, ks0 ⊆ ro1, ∀ key1. (key1 ∈ ri0 ∧ ¬ key1 ∈ ks0 ∧ (¬ key1.data? ∨ ¬ inodekey(key1.ino) ∈ ks0) ↔ key1 ∈ ri1 ⊖ ro1) ∧ (key1 ∈ ri0 ∧ key1.data? ∧ inodekey(key1.ino) ∈ ks0 ⊃ (∅)[key1];(key1 ∈ ks0 ⊃ (∅)[key1];ri0[key1])) = (ri1 ⊖ ro1)[key1] ⊦ # ks0 = 0, # ro1 = 0, ks0 = ∅, ro1 = ∅, (key0 ∈ ((ri0 \ datakeys(key, ri0)) -- key) ⊖ (ks0 -- key) ↔ key0 ∈ ri1 ⊖ ro1) ∧ (((ri0 \ datakeys(key, ri0)) -- key) ⊖ (ks0 -- key))[key0] = (ri1 ⊖ ro1)[key0], key0 ∈ ri0 ∧ ¬ key0 ∈ ks0 ∧ ¬ key0.data?

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: aubifs-base name: dels-with-data seq: ⊦ ri ⊖ ks = (ri \ ks) \ datakeys(ks, ri) subst: [ks, ri] → [ro1, ri1] flags: <all paths>

Additional information

Used terms: ro1, ri1