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Proof step 7 from proof prepost-add-log-leb (previous step)

m5 + # lpt = # avol, avol[m6] = mapped(buf1), avol[m2] = mapped(buf0), avol[0] = mapped(buf), avol0 = avol, m = LEB_SIZE, m0 = EB_PAGE_SIZE, m1 = m8, sb = mksb(adr, m7, m6, m2, m3, m4, m5), disk-layout(mksb(adr, m7, m6, m2, m3, m4, m5), # lpt), ebm-vol-inv(avol), is-encoded(mksb(adr, m7, m6, m2, m3, m4, m5), buf), is-encoded(lpt, lebs(avol, m4, lptlebs(# lpt, LEB_SIZE))), is-encoded(log, buf1), is-encoded-pad(orphans, m3, buf0), mapped-full?(avol, m4, lptlebs(# lpt, LEB_SIZE)), logoff ≠ LEB_SIZE → # buf1 = logoff ⊦ ⟪err := ECOMMIT⟫ ( (err = ESUCCESS ∨ ⌊err⌋ ) ∧ ebm-vol-inv(avol) ∧ subarray(avol, m5, # lpt) = subarray(avol0, m5, # lpt) ∧ ( err = ESUCCESS → m5 + # lpt = # avol ∧ avol[0].mapped? ∧ is-encoded(mksb(adr, m7, m6, m2, m3, m4, m5), avol[0].data) ∧ avol[m2].mapped? ∧ is-encoded-pad(orphans, m3, avol[m2].data) ∧ avol[m6].mapped? ∧ (logoff ≠ LEB_SIZE → # avol[m6].data = logoff) ∧ is-encoded(log + m8 ', avol[m6].data) ∧ mapped-full?(avol, m4, lptlebs(# lpt, LEB_SIZE)) ∧ is-encoded(lpt, lebs(avol, m4, lptlebs(# lpt, LEB_SIZE)))) ∧ ( err ≠ ESUCCESS → m5 + # lpt = # avol ∧ avol[0].mapped? ∧ is-encoded(mksb(adr, m7, m6, m2, m3, m4, m5), avol[0].data) ∧ avol[m2].mapped? ∧ is-encoded-pad(orphans, m3, avol[m2].data) ∧ avol[m6].mapped? ∧ (logoff ≠ LEB_SIZE → # avol[m6].data = logoff) ∧ is-encoded(log, avol[m6].data) ∧ mapped-full?(avol, m4, lptlebs(# lpt, LEB_SIZE)) ∧ is-encoded(lpt, lebs(avol, m4, lptlebs(# lpt, LEB_SIZE))))), logoff + m0 ≤ m

Heuristic symbolic execution applied rule assign right

And closed the goal!

Rule argument

Additional information

Used simplifier rules: ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ ESUCCESS ≠ ECOMMIT; (s)% ⊦ ⌊ECOMMIT⌋ ; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ EB_PAGE_SIZE + n = 0 ↔ false; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ mapped(buf).mapped?; (s)% ⊦ mapped(buf).data = buf; (s)%⊦ is-encoded-pad(ns0, n, buf) → (is-encoded-pad(ns1, n, buf) ↔ ns0 = ns1); (s)% ⊦ is-encoded(nx0, buf) → (is-encoded(nx1, buf) ↔ nx0 = nx1); (s)