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Proof step 2 from proof reduce-initial (previous step)

ubi-io-initial(apebs) ⊦ ubi-io-initial(apebs[n, apeb]) ↔ n < # apebs ∧ ubi-io-peb-initial(apebs[n]) → ubi-io-peb-initial(apeb)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
∀ n0. n0 < # apebs → # apebs[n0].data = LEB_SIZE ∧ ( ¬ apebs[n0].bad → (apebs[n0].echdr = empty → apebs[n0].vidhdr = empty) ∧ (apebs[n0].echdr ≠ garbage ∧ apebs[n0].vidhdr = empty → apebs[n0].fill = 0) ∧ apebs[n0].fill ≤ LEB_SIZE ∧ is-aligned(apebs[n0].fill, EB_PAGE_SIZE) ∧ subarray(apebs[n0].data, apebs[n0].fill, LEB_SIZE - apebs[n0].fill) = mkempbuf(LEB_SIZE - apebs[n0].fill)) ∧ (¬ apebs[n0].bad → apebs[n0].echdr.valid? ∧ apebs[n0].vidhdr = empty) ⊦ (∀ n0. n0 < # apebs → # apebs[n, apeb][n0].data = LEB_SIZE ∧ ( ¬ apebs[n, apeb][n0].bad → (apebs[n, apeb][n0].echdr = empty → apebs[n, apeb][n0].vidhdr = empty) ∧ (apebs[n, apeb][n0].echdr ≠ garbage ∧ apebs[n, apeb][n0].vidhdr = empty → apebs[n, apeb][n0].fill = 0) ∧ apebs[n, apeb][n0].fill ≤ LEB_SIZE ∧ is-aligned(apebs[n, apeb][n0].fill, EB_PAGE_SIZE) ∧ subarray(apebs[n, apeb][n0].data, apebs[n, apeb][n0].fill, LEB_SIZE - apebs[n, apeb][n0].fill) = mkempbuf(LEB_SIZE - apebs[n, apeb][n0].fill)) ∧ (¬ apebs[n, apeb][n0].bad → apebs[n, apeb][n0].echdr.valid? ∧ apebs[n, apeb][n0].vidhdr = empty)) ↔ n < # apebs ∧ # apebs[n].data = LEB_SIZE ∧ ( ¬ apebs[n].bad → (apebs[n].echdr = empty → apebs[n].vidhdr = empty) ∧ (apebs[n].echdr ≠ garbage ∧ apebs[n].vidhdr = empty → apebs[n].fill = 0) ∧ apebs[n].fill ≤ LEB_SIZE ∧ is-aligned(apebs[n].fill, EB_PAGE_SIZE) ∧ subarray(apebs[n].data, apebs[n].fill, LEB_SIZE - apebs[n].fill) = mkempbuf(LEB_SIZE - apebs[n].fill)) ∧ (¬ apebs[n].bad → apebs[n].echdr.valid? ∧ apebs[n].vidhdr = empty) → # apeb.data = LEB_SIZE ∧ ( ¬ apeb.bad → (apeb.echdr = empty → apeb.vidhdr = empty) ∧ (apeb.echdr ≠ garbage ∧ apeb.vidhdr = empty → apeb.fill = 0) ∧ apeb.fill ≤ LEB_SIZE ∧ is-aligned(apeb.fill, EB_PAGE_SIZE) ∧ subarray(apeb.data, apeb.fill, LEB_SIZE - apeb.fill) = mkempbuf(LEB_SIZE - apeb.fill)) ∧ (¬ apeb.bad → apeb.echdr.valid? ∧ apeb.vidhdr = empty)

Rule argument

Additional information

Used simplifier rules: initial: ⊦ ubi-io-initial(apebs) ↔ (∀ n. n < # apebs → ubi-io-peb-initial(apebs[n]));%peb-initial: ⊦ ubi-io-peb-initial(apeb) ↔ ubi-io-peb-inv(apeb) ∧ (¬ apeb.bad → apeb.echdr.valid? ∧ apeb.vidhdr = empty);%peb-inv: ⊦ ubi-io-peb-inv(apeb) ↔ # apeb.data = LEB_SIZE ∧ ( ¬ apeb.bad → (apeb.echdr = empty → apeb.vidhdr = empty) ∧ (apeb.echdr ≠ garbage ∧ apeb.vidhdr = empty → apeb.fill = 0) ∧ apeb.fill ≤ LEB_SIZE ∧ is-aligned(apeb.fill, EB_PAGE_SIZE) ∧ subarray(apeb.data, apeb.fill, LEB_SIZE - apeb.fill) = mkempbuf(LEB_SIZE - apeb.fill));% ⊦ # apebs[n, apeb] = # apebs; (s)