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Proof step 107 from proof inv-format (previous step)

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

User applied rule cut formula

And obtained the following new goals

Proof step 108:
# lebs(avol0, 5, lptlebs(# lpt, LEB_SIZE)) = lptsize(# lpt, LEB_SIZE), # avol0 = # lpt + 5 + 2 * 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], err = ESUCCESS, 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), 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 ≤ # avol0, 5 + lptlebs(# lpt, LEB_SIZE) ≤ # avol0, err = ESUCCESS → 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) ∧ avol[0] = mapped(buf), err ≠ ESUCCESS → avol = avol0, err = ESUCCESS ∨ ⌊err⌋ ⊦ ( 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 = # avol ∧ avol[0].mapped? ∧ is-encoded (((((((sb0.indexaddr:= adr).maxino:= m1).log:= 1).orph:= 3).orphsize:= 0).lpt:= 5).main:= (5 + 2 * lptlebs(# lpt, LEB_SIZE)), avol[0].data) ∧ avol[3].mapped? ∧ is-encoded-pad(orphans, 0, avol[3].data) ∧ avol[1].mapped? ∧ is-encoded(log, avol[1].data) ∧ mapped-full?(avol, 5, lptlebs(# lpt0, LEB_SIZE)) ∧ is-encoded(lpt0, lebs(avol, 5, lptlebs(# lpt0, LEB_SIZE))))) ∧ ( err = ESUCCESS → subarray(avol, 5 + 2 * lptlebs(# lpt, LEB_SIZE), # avol - 5 + 2 * lptlebs(# lpt, LEB_SIZE)) = fill(mkavolume(# lpt), unmapped) ∧ is-encoded(lpt, lebs(avol, 5, lptlebs(# avol - 5 + 2 * lptlebs(# lpt, LEB_SIZE), LEB_SIZE))) ∧ avol[1].data = mkbuf(0) ∧ avol[3].data = mkbuf(0))

Rule argument

fma: err = ESUCCESS

Additional information

Used simplifier rules: ⊦ ⌊err⌋ → err ≠ ESUCCESS; (s) Used formulas: err = ESUCCESS