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Proof step 82 from proof inv-recover (previous step)

# avol2 = # avol0, # lpt2 = # avol0, # avol = # avol0, # lpt3 = # avol0, (lpf0 = LP_FREE ⊃ mklp(m2, m3, LP_FREE, m4) ;(lpf0 = LP_INDEX_NODES ∧ m2 ≠ 0 ⊃ mklp(m2, LEB_SIZE, LP_INDEX_NODES, m4);(m2 = 0 ⊃ mklp(0, 0, LP_FREE, m4);mklp(m2, m3, lpf0, m4))) ) = mklp(m, m0, lpf, m1), lpt3[n] = mklp(m2, m3, lpf0, m4), gc-heap(replay-lpt(replay-log(lpt3, log2), log2, # avol0), log2) = keyset(gch), keyset(gch1) = gc-heap(lpt2, log2), LEB_SIZE < m0, n < # avol0, avol-replay-lpt-unchanged(avol, avol2, replay-log(lpt3, log2), log2), awbuf-inv(avol0, bleb1), awbuf-inv(avol2, nobuffer), bin-heap-inv(gch, lpt), bin-heap-inv(gch1, lpt2), buf-ro-rw-mode(isbuf1, bleb1, lpt2, avol0), bufs-log-only(bleb1, log2, lpt2), freelist-cons(replay-lpt(replay-log(lpt3, log2), log2, # avol0), freelist), freelist-cons(lpt2, log5), id-idx(replay-lpt(replay-log(lpt3, log2), log2, # avol0), lpt), log-group-block(log2, replay-lpt(replay-log(lpt3, log2), log2, # avol0)), 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(avol), synced(avol0), valid-indices(lpt3, log2), avol ↓ avol0 ⊦ dups(log2), n ∈ log2

User applied rule case distinction

And obtained the following new goals

Proof step 83:
# lpt3 = # avol0, # avol = # avol0, # lpt2 = # avol0, # avol2 = # avol0, (lpf0 = LP_INDEX_NODES ∧ m2 ≠ 0 ⊃ mklp(m2, LEB_SIZE, LP_INDEX_NODES, m4);(m2 = 0 ⊃ mklp(0, 0, LP_FREE, m4);mklp(m2, m3, lpf0, m4))) = mklp(m, m0, lpf, m1), lpt3[n] = mklp(m2, m3, lpf0, m4), gc-heap(replay-lpt(replay-log(lpt3, log2), log2, # avol0), log2) = keyset(gch), keyset(gch1) = gc-heap(lpt2, log2), n < # avol0, LEB_SIZE < m0, avol-replay-lpt-unchanged(avol, avol2, replay-log(lpt3, log2), log2), awbuf-inv(avol2, nobuffer), awbuf-inv(avol0, bleb1), bin-heap-inv(gch1, lpt2), bin-heap-inv(gch, lpt), buf-ro-rw-mode(isbuf1, bleb1, lpt2, avol0), bufs-log-only(bleb1, log2, lpt2), freelist-cons(lpt2, log5), freelist-cons(replay-lpt(replay-log(lpt3, log2), log2, # avol0), freelist), id-idx(replay-lpt(replay-log(lpt3, log2), log2, # avol0), lpt), log-group-block(log2, lpt2), log-group-block(log2, replay-lpt(replay-log(lpt3, log2), log2, # avol0)), 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 ⊦ lpf0 = LP_FREE, dups(log2), n ∈ log2

Rule argument

pos: left 5

Additional information

Used simplifier rules: ⊦ mklp(m, m0, lpf, m1) = mklp(m2, m3, lpf0, m4) ↔ m = m2 ∧ m0 = m3 ∧ lpf = lpf0 ∧ m1 = m4; (ws)%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ m < n → (n ≤ m ↔ false); (s)%free-unref-at: n < # lpt ⊦ lpt-free-unref(lpt) ∧ lpt[n] = mklp(n0, n1, LP_FREE, n2) → n0 = 0; (forward) from specification persistence-base%n < # lpt ⊦ lpt[n] = mklp(n0, n1, lpf, n2) ∧ lpt-leb-size(lpt) → ¬ LEB_SIZE < n1; (s)