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Proof step 10 from proof prepost-add-log-leb (previous step)

m5 + # lpt = # avol, avol[m6] = mapped(buf1), avol[m2] = mapped(buf0), avol[0] = mapped(buf2), buf = mkbuf(EB_PAGE_SIZE), # buf1 ≠ LEB_SIZE, 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), buf2), 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)), # buf1 + EB_PAGE_SIZE ≤ LEB_SIZE ⊦ ⟪encode_ref_node#(EB_PAGE_SIZE, rnode(m8); buf; err); avol0 := avol; logoff := # buf1; if err = ESUCCESS then {ebm_avol_write#(m6, logoff, 0, EB_PAGE_SIZE, buf; avol; err); if err = ESUCCESS then logoff := logoff + EB_PAGE_SIZE else {logoff := LEB_SIZE; debug#("persistence-io: failed to add LEB " + m8.toString + " to log")}}⟫ ( (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)))))

User applied rule insert program lemma

And obtained the following new goals

Proof step 11:
EB_PAGE_SIZE ≤ # buf, buf0 = buf ⊦ ⟪encode_ref_node#(EB_PAGE_SIZE, rnd; buf; err)⟫ ((err = ESUCCESS ∨ ⌊err⌋ ) ∧ # buf = # buf0 ∧ (err = ESUCCESS → is-encoded(rnd, subarray(buf, 0, EB_PAGE_SIZE))))
Proof step 12:
m5 + # lpt = # avol, avol[0] = mapped(buf2), avol[m2] = mapped(buf0), avol[m6] = mapped(buf1), buf = mkbuf(EB_PAGE_SIZE), buf = buf, buf3 = buf, rnd0 = rnode(m8), disk-layout(mksb(adr, m7, m6, m2, m3, m4, m5), # lpt), ebm-vol-inv(avol), is-encoded(log, buf1), is-encoded(lpt, lebs(avol, m4, lptlebs(# lpt, LEB_SIZE))), is-encoded(mksb(adr, m7, m6, m2, m3, m4, m5), buf2), is-encoded-pad(orphans, m3, buf0), mapped-full?(avol, m4, lptlebs(# lpt, LEB_SIZE)), # buf1 + EB_PAGE_SIZE ≤ LEB_SIZE, EB_PAGE_SIZE ≤ # buf ⊦ [encode_ref_node#(EB_PAGE_SIZE, rnode(m8); buf; err)] ( (err = ESUCCESS ∨ ⌊err⌋ ) ∧ # buf = # buf3 ∧ (err = ESUCCESS → is-encoded(rnd0, subarray(buf, 0, EB_PAGE_SIZE))) → ⟪avol0 := avol; logoff := # buf1; if err = ESUCCESS then {ebm_avol_write#(m6, logoff, 0, EB_PAGE_SIZE, buf; avol; err); if err = ESUCCESS then logoff := logoff + EB_PAGE_SIZE else {logoff := LEB_SIZE; debug#("persistence-io: failed to add LEB " + m8.toString + " to log")}}⟫ ( (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)))))), # buf1 = LEB_SIZE

Rule argument

spec: encoding-page-size-nonempty, inst: encoding-ref-node name: encode-contract seq: EB_PAGE_SIZE ≤ # buf, buf0 = buf ⊦ ⟪encode_ref_node#(EB_PAGE_SIZE, rnd; buf; err)⟫ ( (err = ESUCCESS ∨ ⌊err⌋ ) ∧ # buf = # buf0 ∧ ( err = ESUCCESS → is-encoded(rnd, subarray(buf, 0, EB_PAGE_SIZE)))) subst: [rnd, buf, err, buf0] → [rnode(m8), buf, err, buf] flags: <all paths>

Additional information

Used simplifier rules: ⊦ # mkbuf(n) = n; (s)% ⊦ m ≤ m; (s)