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Proof step 76 from proof inv-recover (previous step)

# avol2 = # avol0, # lpt2 = # avol0, # avol = # avol0, # lpt3 = # avol0, (replay-log(lpt3, log2)[n].flags = LP_FREE ∨ n ∈ log2 ⊃ replay-log(lpt3, log2)[n] ;(replay-log(lpt3, log2)[n].flags = LP_INDEX_NODES ∧ replay-log(lpt3, log2)[n].ref-size ≠ 0 ⊃ replay-log(lpt3, log2)[n].size:= LEB_SIZE ;(replay-log(lpt3, log2)[n].ref-size = 0 ⊃ mklp(0, 0, LP_FREE, replay-log(lpt3, log2)[n].gcheapidx);replay-log(lpt3, log2)[n]) ) ) = mklp(m, m0, lpf, m1), 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, # avol0 ≤ # replay-log(lpt3, log2) ⊦ dups(log2)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 77:
# avol2 = # avol0, # lpt2 = # avol0, # avol = # avol0, # lpt3 = # avol0, (lpt3[n].flags = LP_FREE ∨ n ∈ log2 ⊃ replay-log(lpt3, log2)[n] ;(lpt3[n].flags = LP_INDEX_NODES ∧ lpt3[n].ref-size ≠ 0 ⊃ mklp(lpt3[n].ref-size, LEB_SIZE, lpt3[n].flags, lpt3[n].gcheapidx) ;(lpt3[n].ref-size = 0 ⊃ mklp(0, 0, LP_FREE, lpt3[n].gcheapidx);lpt3[n]) ) ) = mklp(m, m0, lpf, m1), 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)

Rule argument

Additional information

Used simplifier rules: elim-lp-upd-size: ⊦ lp.size:= n = mklp(lp.ref-size, n, lp.flags, lp.gcheapidx);% ⊦ m ≤ m; (s)% ⊦ m < n → n ≠ 0; (s)%fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ # replay-log(lpt, nx) = # lpt; (s)%n < # lpt ⊦ ¬ n ∈ nx → replay-log(lpt, nx)[n] = lpt[n]; (s)% ⊦ m < n → (n ≤ m ↔ false); (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)