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Proof step 35 from proof inv-recover (previous step)

# avol = # avol0, # lpt2 = # avol0, # lpt3 = # avol0, keyset(gch1) = gc-heap(lpt2, log2), log = log2, lpt1 = lpt3, awbuf-inv(avol0, bleb1), bin-heap-inv(gch1, lpt2), buf-ro-rw-mode(isbuf1, bleb1, lpt2, avol0), bufs-log-only(bleb1, log2, lpt2), freelist-cons(lpt2, log5), log-group-block(log2, lpt2), lpt-free-unref(lpt3), lpt-free-unref(lpt2), lpt-leb-size(lpt3), lpt-leb-size(lpt2), lpt-ram-flash(lpt2, lpt3, log2), synced(avol0), synced(avol), valid-indices(lpt3, log2), avol ↓ avol0 ⊦ ∀ log, lpt3. lpt3 = replay-log(lpt1, log2) → ⟪persistence_replay_lpt#(log2, LEB_SIZE, 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(lpt1, log2), log2, # avol0)) ∧ lpt-free-unref(lpt1) ∧ freelist-cons(replay-lpt(replay-log(lpt1, log2), log2, # avol0), freelist) ∧ bin-heap-inv(gch, lpt3) ∧ keyset(gch) = gc-heap(replay-lpt(replay-log(lpt1, log2), log2, # avol0), log2) ∧ # lpt3 = # avol ∧ log-group-block(log2, lpt3) ∧ lpt-leb-size(replay-lpt(replay-log(lpt1, log2), log2, # avol0)) ∧ lpt-leb-size(lpt1) ∧ lpt-ram-flash(lpt3, lpt1, log2) ∧ awbuf-inv(avol, nobuffer) ∧ # lpt1 = # avol ∧ # avol = # avol0 ∧ id-idx(replay-lpt(replay-log(lpt1, log2), log2, # avol0), lpt3)), dups(log2)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 36:
# avol = # avol0, # lpt2 = # avol0, # lpt3 = # avol0, keyset(gch1) = gc-heap(lpt2, log2), lpt = replay-log(lpt3, log2), awbuf-inv(avol0, bleb1), bin-heap-inv(gch1, lpt2), buf-ro-rw-mode(isbuf1, bleb1, lpt2, avol0), bufs-log-only(bleb1, log2, lpt2), freelist-cons(lpt2, log5), log-group-block(log2, lpt2), lpt-free-unref(lpt3), lpt-free-unref(lpt2), lpt-leb-size(lpt3), lpt-leb-size(lpt2), lpt-ram-flash(lpt2, lpt3, log2), synced(avol0), synced(avol), valid-indices(lpt3, log2), avol ↓ avol0, ¬ dups(log2) ⊦ ⟪persistence_replay_lpt#(log2, LEB_SIZE, adr2, m4, log2, lpt3, ns2, nobuffer, false; lpt, avol); persistence_create_freelist#(lpt; freelist); persistence_create_gcheap#(log2; lpt, gch)⟫ ( freelist-cons(replay-lpt(replay-log(lpt3, log2), log2, # avol0), freelist) ∧ bin-heap-inv(gch, lpt) ∧ keyset(gch) = gc-heap(replay-lpt(replay-log(lpt3, log2), log2, # avol0), log2) ∧ # lpt = # avol ∧ log-group-block(log2, lpt) ∧ lpt-leb-size(replay-lpt(replay-log(lpt3, log2), log2, # avol0)) ∧ lpt-ram-flash(lpt, lpt3, log2) ∧ awbuf-inv(avol, nobuffer) ∧ # avol = # avol0 ∧ id-idx(replay-lpt(replay-log(lpt3, log2), log2, # avol0), lpt))

Rule argument

Additional information

Used simplifier rules: ⊦ lpt-free-unref(lpt) → lpt-free-unref(replay-log(lpt, nx)); (s)%n ≤ # lpt ⊦ lpt-free-unref(replay-lpt(lpt, nx, n)) ↔ lpt-free-unref(lpt); (s)% ⊦ ¬ n < n; (s)% ⊦ m < n → n ≠ 0; (s)%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ # replay-log(lpt, nx) = # lpt; (s)