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

# lpt1 = # avol, # lpt0 = # avol, EB_PAGE_SIZE = # buf1 + # buf0 % EB_PAGE_SIZE, lpt1[n] = mklp(m3, # buf0, lpf, m4), avol[n] = mapped(buf0), ¬ isbuf1, keyset(gch) = gc-heap(lpt1, log0), buf1 ≠ mkbuf(0), lpf ≠ LP_FREE, n < # avol, abs-padding(buf1), awbuf-inv(avol, buffered(n)), bin-heap-inv(gch, lpt1), buf-ro-rw-mode(false, buffered(n), lpt1, avol), bufs-log-only(buffered(n), log0, lpt1), freelist-cons(lpt1, freelist), is-aligned(# buf0, 2 * NODE_HEADER_SIZE), log-group-block(log0, lpt1), lpt-free-unref(lpt1), lpt-free-unref(lpt0), lpt-leb-size(lpt1), lpt-leb-size(lpt0), lpt-ram-flash(lpt1, lpt0, log0), # buf0 ≤ LEB_SIZE, ¬ is-aligned(# buf0, EB_PAGE_SIZE) ⊦ ⟪awbuf_write_buf#(# buf1, buf1, adr, m2, log0, lpt0, ns, buffered(n); avol, isbuf1; err); m := EB_PAGE_SIZE - lpt1[buffered(n).leb].size % EB_PAGE_SIZE; bleb1 := buffered(n); if err = ESUCCESS then lpt1[bleb1.leb] := mklp(lpt1[bleb1.leb].ref-size, lpt1[bleb1.leb].size + m, lpt1[bleb1.leb].flags, lpt1[bleb1.leb].gcheapidx) else {debug#("persistence: flushing of LEB " + bleb1.leb.toString + " failed"); lpt1[bleb1.leb] := mklp(lpt1[bleb1.leb].ref-size, LEB_SIZE, lpt1[bleb1.leb].flags, lpt1[bleb1.leb].gcheapidx); awbuf_enter_readonly#(adr, m2, log0, avol, lpt0, ns, bleb1; ; isbuf1)}⟫ ( lpt-free-unref(lpt1) ∧ freelist-cons(lpt1, freelist) ∧ bin-heap-inv(gch, lpt1) ∧ keyset(gch) = gc-heap(lpt1, log0) ∧ bufs-log-only(bleb1, log0, lpt1) ∧ # lpt1 = # avol ∧ log-group-block(log0, lpt1) ∧ buf-ro-rw-mode(isbuf1, bleb1, lpt1, avol) ∧ lpt-leb-size(lpt1) ∧ lpt-ram-flash(lpt1, lpt0, log0) ∧ awbuf-inv(avol, bleb1) ∧ # lpt0 = # avol)

User applied rule insert program lemma

And obtained the following new goals

Rule argument

spec: awbuf-asm name: inv-write-buf seq: awbuf-inv(avol, bleb), # lpt = # avol, bleb ≠ nobuffer, # avol[bleb.leb].data + n ≤ LEB_SIZE, n ≤ # buf ⊦ ⟪awbuf_write_buf# (n, buf, adr, m, nx, lpt, ns, bleb; avol, isbuf; err)⟫ (awbuf-inv(avol, bleb) ∧ # lpt = # avol) subst: [bleb, ns, lpt, nx, m, adr, buf, n, isbuf, avol, err] → [buffered(n), ns, lpt0, log0, m2, adr, buf1, # buf1, isbuf1, avol, err] flags: <all paths>

Additional information

Used simplifier rules: flush-padding-space-write: ⊦ n < # avol ∧ avol[n] = mapped(buf0) ∧ awbuf-inv(avol, bleb) ∧ EB_PAGE_SIZE = # buf1 + # buf0 % EB_PAGE_SIZE ∧ ¬ is-aligned(# buf0, EB_PAGE_SIZE) → ¬ LEB_SIZE < # buf0 + # buf1;% ⊦ nobuffer ≠ buffered(m); (s)% ⊦ buffered(m).leb = m; (s)% ⊦ m ≤ m; (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat% ⊦ mapped(buf).data = buf; (s)% ⊦ m < m + n ↔ n ≠ 0; (s)% ⊦ # buf = 0 ↔ buf = mkbuf(0); (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic