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Proof step 16 from proof inv-recover (previous step)

# lpt1 = # avol0, # lpt3 = # avol0, isbuf ↔ false, adr = adr2, adr0 = adr, bleb = nobuffer, err = err0, err = ESUCCESS, keyset(gch1) = gc-heap(lpt1, log2), log = log2, log0 = log, log3 = log0, log4 = log1, lpt = lpt3, lpt0 = lpt, m = m4, m0 = m, m3 = m1, ns = ns2, ns0 = ns, awbuf-inv(avol0, bleb1), bin-heap-inv(gch1, lpt1), buf-ro-rw-mode(isbuf1, bleb1, lpt1, avol0), bufs-log-only(bleb1, log2, lpt1), freelist-cons(lpt1, log5), log-group-block(log2, lpt1), lpt-free-unref(lpt1), lpt-free-unref(lpt3), lpt-leb-size(lpt1), lpt-leb-size(lpt3), lpt-ram-flash(lpt1, lpt3, log2), synced(avol0), avol ↓ avol0, err = ESUCCESS → synced(avol) ∧ awbuf-inv(avol, bleb) ∧ # lpt = # avol, ⌊err0⌋ ∨ err0 = ESUCCESS ⊦ ⟪awbuf_get_leb_size#(adr, m, log, avol, lpt, ns, bleb, isbuf; ; m2); let log1 = log3 in persistence_replay_log#(m2; log1, lpt0); persistence_replay_lpt#(log3, m2, adr, m, log, lpt, ns, bleb, isbuf; lpt0, avol); persistence_create_freelist#(lpt0; freelist); persistence_create_gcheap#(log3; lpt0, gch)⟫ ( ( err = ESUCCESS → synced(avol) ∧ lpt-free-unref(lpt0) ∧ lpt-free-unref(lpt) ∧ freelist-cons(lpt0, freelist) ∧ log3 = log ∧ bin-heap-inv(gch, lpt0) ∧ keyset(gch) = gc-heap(lpt0, log) ∧ bufs-log-only(bleb, log, lpt0) ∧ # lpt0 = # avol ∧ ¬ dups(log) ∧ log-group-block(log, lpt0) ∧ buf-ro-rw-mode(isbuf, bleb, lpt0, avol) ∧ lpt-leb-size(lpt0) ∧ lpt-leb-size(lpt) ∧ lpt-ram-flash(lpt0, lpt, log) ∧ m2 = LEB_SIZE ∧ awbuf-inv(avol, bleb) ∧ # lpt = # avol) ∧ (err = ESUCCESS ∨ ⌊err⌋ ) ∧ ( err = ESUCCESS → # avol = # avol0 ∧ adr0 = adr2 ∧ adr = adr2 ∧ m0 = m4 ∧ m = m4 ∧ log0 = log2 ∧ log = log2 ∧ ns0 = ns2 ∧ ns = ns2 ∧ lpt = lpt3 ∧ bleb = nobuffer ∧ id-idx(replay-lpt(replay-log(lpt3, log2), log2, # avol0), lpt0))), dups(log2)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 17:
# avol = # avol0, # lpt1 = # avol0, # lpt3 = # avol0, keyset(gch1) = gc-heap(lpt1, log2), awbuf-inv(avol0, bleb1), bin-heap-inv(gch1, lpt1), buf-ro-rw-mode(isbuf1, bleb1, lpt1, avol0), bufs-log-only(bleb1, log2, lpt1), freelist-cons(lpt1, log5), log-group-block(log2, lpt1), lpt-free-unref(lpt3), lpt-free-unref(lpt1), lpt-leb-size(lpt3), lpt-leb-size(lpt1), lpt-ram-flash(lpt1, lpt3, log2), synced(avol0), synced(avol), avol ↓ avol0, ¬ dups(log2) ⊦ ⟪awbuf_get_leb_size#(adr2, m4, log2, avol, lpt3, ns2, nobuffer, false; ; m2); let log1 = log2 in {lpt1 := lpt3; lpt0 := lpt3; persistence_replay_log#(m2; log1, lpt3)}; persistence_replay_lpt#(log2, m2, adr2, m4, log2, lpt1, ns2, nobuffer, false; lpt3, avol); persistence_create_freelist#(lpt3; freelist); persistence_create_gcheap#(log2; lpt3, gch)⟫ ( lpt-free-unref(replay-lpt(replay-log(lpt0, log2), log2, # avol0)) ∧ lpt-free-unref(lpt0) ∧ freelist-cons(replay-lpt(replay-log(lpt0, log2), log2, # avol0), freelist) ∧ bin-heap-inv(gch, lpt3) ∧ keyset(gch) = gc-heap(replay-lpt(replay-log(lpt0, log2), log2, # avol0), log2) ∧ # lpt3 = # avol ∧ log-group-block(log2, lpt3) ∧ lpt-leb-size(replay-lpt(replay-log(lpt0, log2), log2, # avol0)) ∧ lpt-leb-size(lpt0) ∧ lpt-ram-flash(lpt3, lpt0, log2) ∧ m2 = LEB_SIZE ∧ awbuf-inv(avol, nobuffer) ∧ # lpt0 = # avol ∧ # avol = # avol0 ∧ lpt1 = lpt0 ∧ id-idx(replay-lpt(replay-log(lpt0, log2), log2, # avol0), lpt3))

Rule argument

Additional information

Used simplifier rules: ⊦ id-idx(lpt0, lpt1) → (lpt-leb-size(lpt1) ↔ lpt-leb-size(lpt0)); (s)% ⊦ id-idx(lpt0, lpt1) → gc-heap(lpt1, nx) = gc-heap(lpt0, nx); (s)%⊦ id-idx(lpt0, lpt1) → (freelist-cons(lpt1, freelist) ↔ freelist-cons(lpt0, freelist)); (s)% ⊦ id-idx(lpt0, lpt1) → (lpt-free-unref(lpt1) ↔ lpt-free-unref(lpt0)); (s)% ⊦ buf-ro-rw-mode(boolvar, nobuffer, lpt, avol); (s)% ⊦ bufs-log-only(nobuffer, nx, lpt); (s)% ⊦ awbuf-inv(avol, nobuffer) → (synced(avol) ↔ true); (ss)% ⊦ avol1 ↓ avol0 ∧ awbuf-inv(avol0, bleb) → awbuf-inv(avol1, nobuffer); (s)% ⊦ ¬ ⌊ESUCCESS⌋ ; (s)