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Proof step 99 from proof inv-format (previous step)

# lebs(avol0, 5, lptlebs(# lpt, LEB_SIZE)) = lptsize(# lpt, LEB_SIZE), # avol0 = # lpt + 5 + 2 * lptlebs(# lpt, LEB_SIZE), # avol0 = n0 + 5 + lptlebs(# lpt, LEB_SIZE), avol0[4] = fill(mkavolume(# avol0), unmapped)[4], avol0[3] = mapped(mkbuf(0)), avol0[2] = fill(mkavolume(# avol0), unmapped)[2], avol0[1] = mapped(mkbuf(0)), avol0[0] = fill(mkavolume(# avol0), unmapped)[0], ebm-vol-inv(fill(mkavolume(# avol0), unmapped)[1, mapped(mkbuf(0))][3, mapped(mkbuf(0))]), ebm-vol-inv(fill(mkavolume(# avol0), unmapped)), ebm-vol-inv(fill(mkavolume(# avol0), unmapped)[1, mapped(mkbuf(0))]), ebm-vol-inv(avol0), is-encoded(lpt, lebs(avol0, 5, lptlebs(# lpt, LEB_SIZE))), mapped-full?(avol0, 5, lptlebs(# lpt, LEB_SIZE)), range=(avol0, 5 + lptlebs(# lpt, LEB_SIZE), fill(mkavolume(# avol0), unmapped), 5 + lptlebs(# lpt, LEB_SIZE), n0), 5 ≤ # avol0, 5 + lptlebs(# lpt, LEB_SIZE) ≤ # avol0 ⊦ ⟪persistence_io_write_superblock# (((((((sb0.indexaddr:= adr).maxino:= m1).log:= 1).orph:= 3).orphsize:= 0).lpt:= 5).main:= (5 + 2 * lptlebs(# lpt, LEB_SIZE)), EB_PAGE_SIZE, LEB_SIZE ; avol0 ; err); logoff := LEB_SIZE⟫ ( ( err = ESUCCESS → (∃ lpt0, log, orphans. disk-layout (((((((sb0.indexaddr:= adr).maxino:= m1).log:= 1).orph:= 3).orphsize:= 0).lpt:= 5).main:= (5 + 2 * lptlebs(# lpt, LEB_SIZE)), # lpt0) ∧ (5 + 2 * lptlebs(# lpt, LEB_SIZE)) + # lpt0 = # avol0 ∧ avol0[0].mapped? ∧ is-encoded (((((((sb0.indexaddr:= adr).maxino:= m1).log:= 1).orph:= 3).orphsize:= 0).lpt:= 5).main:= (5 + 2 * lptlebs(# lpt, LEB_SIZE)), avol0[0].data) ∧ avol0[3].mapped? ∧ is-encoded-pad(orphans, 0, avol0[3].data) ∧ avol0[1].mapped? ∧ (logoff ≠ LEB_SIZE → # avol0[1].data = logoff) ∧ is-encoded(log, avol0[1].data) ∧ mapped-full?(avol0, 5, lptlebs(# lpt0, LEB_SIZE)) ∧ is-encoded(lpt0, lebs(avol0, 5, lptlebs(# lpt0, LEB_SIZE)))) ∧ ebm-vol-inv(avol0)) ∧ (err = ESUCCESS ∨ ⌊err⌋ ) ∧ ( err = ESUCCESS → subarray(avol0, 5 + 2 * lptlebs(# lpt, LEB_SIZE), # avol0 - 5 + 2 * lptlebs(# lpt, LEB_SIZE)) = fill(mkavolume(# lpt), unmapped) ∧ is-encoded(lpt, lebs(avol0, 5, lptlebs(# avol0 - 5 + 2 * lptlebs(# lpt, LEB_SIZE), LEB_SIZE))) ∧ avol0[1].data = mkbuf(0) ∧ avol0[3].data = mkbuf(0)))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: ⊦ m + m = 2 * m; (s)%mult-c: ⊦ m * n = n * m; from specification nat-mult%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult% ⊦ m0 * 1 = m0; (s)%m2 ≠ 0 ⊦ (* m2) * m + n = m + n0 ↔ (m2 - 1) * m + n = n0; (s)%eqs: ⊦ m = n + n0 ∧ m = n + n1 → n0 = n1; (forward) from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic