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Proof step 36 from proof inv-recover (previous step)

# 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))

User applied rule insert program lemma

And obtained the following new goals

Proof step 37:
lpt0 = lpt, avol0 = avol, awbuf-inv(avol, nobuffer), # lpt = # avol, synced(avol) ⊦ ⟪persistence_replay_lpt#(nx, LEB_SIZE, adr, m0, log0, lpt1, ns, nobuffer, boolvar; lpt, avol)⟫ (lpt = replay-lpt(lpt0, nx, # lpt0) ∧ awbuf-inv(avol, nobuffer) ∧ avol-replay-lpt-unchanged(avol0, avol, lpt0, nx))
Proof step 38:
# lpt3 = # avol0, # lpt2 = # avol0, # avol = # avol0, # lpt = # avol, boolvar0 ↔ false, adr0 = adr2, avol = avol, avol1 = avol, keyset(gch1) = gc-heap(lpt2, log2), log = log2, lpt = replay-log(lpt3, log2), lpt = lpt, lpt4 = lpt, lpt5 = lpt3, m = m4, ns0 = ns2, nx0 = log2, awbuf-inv(avol0, bleb1), awbuf-inv(avol, nobuffer), 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(lpt2), lpt-free-unref(lpt3), lpt-leb-size(lpt2), lpt-leb-size(lpt3), lpt-ram-flash(lpt2, lpt3, log2), synced(avol0), synced(avol), valid-indices(lpt3, log2), avol ↓ avol0 ⊦ [persistence_replay_lpt#(log2, LEB_SIZE, adr2, m4, log2, lpt3, ns2, nobuffer, false; lpt, avol)] ( lpt = replay-lpt(lpt4, nx0, # lpt4) ∧ awbuf-inv(avol, nobuffer) ∧ avol-replay-lpt-unchanged(avol1, avol, lpt4, nx0) → ⟪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))), dups(log2)

Rule argument

spec: <toplevel> name: prepost-replay-lpt seq: lpt0 = lpt, avol0 = avol, awbuf-inv(avol, nobuffer), # lpt = # avol, synced(avol) ⊦ ⟪persistence_replay_lpt# (nx, LEB_SIZE, adr, m0, log0, lpt1, ns, nobuffer, boolvar ; lpt, avol)⟫ ( lpt = replay-lpt(lpt0, nx, # lpt0) ∧ awbuf-inv(avol, nobuffer) ∧ avol-replay-lpt-unchanged(avol0, avol, lpt0, nx)) subst: [boolvar, ns, lpt1, log0, m0, adr, nx, avol, lpt, lpt0, avol0] → [false, ns2, lpt3, log2, m4, adr2, log2, avol, lpt, lpt, avol] flags: <all paths>

Additional information

Used simplifier rules: ⊦ avol1 ↓ avol0 ∧ awbuf-inv(avol0, bleb) → awbuf-inv(avol1, nobuffer); (s)% ⊦ # replay-log(lpt, nx) = # lpt; (s)% ⊦ avol1 ↓ avol0 ∧ # avol0 = n → (n = # avol1 ↔ true); (ss)% ⊦ synced(avol0) ∧ avol1 ↓ avol0 → (synced(avol1) ↔ true); (ss)