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Proof step 112 from proof inv-format (previous step)

# avol0 = # lpt + 5 + 2 * lptlebs(# lpt, LEB_SIZE), # avol = # avol0, # lebs(avol0, 5, lptlebs(# lpt, LEB_SIZE)) = lptsize(# lpt, LEB_SIZE), avol[0] = mapped(buf), 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], sb0 = mksb(adr0, m, m0, m2, m3, m4, m5), 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), ebm-vol-inv(avol), id○(avol, avol0, 0), is-encoded(((((((sb0.indexaddr:= adr).maxino:= m1).log:= 1).orph:= 3).orphsize:= 0).lpt:= 5).main:= (5 + 2 * lptlebs(# lpt, LEB_SIZE)), buf), 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), lptlebs(# lpt, LEB_SIZE) + # lpt), 5 + 2 * lptlebs(# lpt, LEB_SIZE) ≤ # avol0, 5 ≤ # avol0, 5 + lptlebs(# lpt, LEB_SIZE) ≤ # avol0 ⊦ (∃ 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 ∧ avol[3].mapped? ∧ is-encoded-pad(orphans, 0, avol[3].data) ∧ avol[1].mapped? ∧ is-encoded(log, avol[1].data) ∧ mapped-full?(avol0, 5, lptlebs(# lpt0, LEB_SIZE)) ∧ is-encoded(lpt0, lebs(avol, 5, lptlebs(# lpt0, LEB_SIZE)))) ∧ subarray(fill(mkavolume(# avol0), unmapped), 5 + 2 * lptlebs(# lpt, LEB_SIZE), # lpt) = fill(mkavolume(# lpt), unmapped) ∧ avol[1].data = mkbuf(0) ∧ avol[3].data = mkbuf(0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m + n = m + n0 ↔ n = n0; (s)% ⊦ SB_LPT = 5; (s)% ⊦ SB_ORPH = 3; (s)%⊦ disk-layout(mksb(adr0, m1, 1, m3, m4, m5, m6), # lpt) ↔ m3 = SB_ORPH ∧ m5 = SB_LPT ∧ m6 = SB_LPT + 2 * lptlebs(# lpt, LEB_SIZE); (s)%⊦ mksb(adr, m, m0, m1, m2, m3, m4).main:= m10 = mksb(adr, m, m0, m1, m2, m3, m10); (s)%⊦ mksb(adr, m, m0, m1, m2, m3, m4).lpt:= m9 = mksb(adr, m, m0, m1, m2, m9, m4); (s)%⊦ mksb(adr, m, m0, m1, m2, m3, m4).orphsize:= m8 = mksb(adr, m, m0, m1, m8, m3, m4); (s)%⊦ mksb(adr, m, m0, m1, m2, m3, m4).orph:= m7 = mksb(adr, m, m0, m7, m2, m3, m4); (s)%⊦ mksb(adr, m, m0, m1, m2, m3, m4).log:= m6 = mksb(adr, m, m6, m1, m2, m3, m4); (s)%⊦ mksb(adr, m, m0, m1, m2, m3, m4).maxino:= m5 = mksb(adr, m5, m0, m1, m2, m3, m4); (s)%⊦ mksb(adr, m, m0, m1, m2, m3, m4).indexaddr:= adr0 = mksb(adr0, m, m0, m1, m2, m3, m4); (s)