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Proof step 26 from proof inv-sync (previous step)

# lpt0 = # avol, # lpt1 = # avol, EB_PAGE_SIZE = n0 + # buf0 % EB_PAGE_SIZE, avol[n] = mapped(buf0), lpt1[n] = mklp(m3, # buf0, lpf, m4), buf = mkbuf(n0), keyset(gch) = gc-heap(lpt1, log0), lpf ≠ LP_FREE, n < # avol, 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(lpt0), lpt-free-unref(lpt1), lpt-leb-size(lpt0), lpt-leb-size(lpt1), lpt-ram-flash(lpt1, lpt0, log0), # buf0 ≤ LEB_SIZE, ¬ is-aligned(# buf0, EB_PAGE_SIZE) ⊦ ⟪persistence_encode_padding_node#(; buf; err); isbuf1 := false; bleb1 := buffered(n); if err = ESUCCESS then {awbuf_write_buf#(# buf, buf, adr, m2, log0, lpt0, ns, bleb1; avol, isbuf1; err); m := EB_PAGE_SIZE - lpt1[bleb1.leb].size % EB_PAGE_SIZE; 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)}} else {debug#("persistence: could not encode padding node"); 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

Proof step 27:
buf0 = buf, is-aligned(# buf, 2 * NODE_HEADER_SIZE), # buf ≥ 2 * NODE_HEADER_SIZE ⊦ ⟪persistence_encode_padding_node#(; buf; err)⟫ ((err = ESUCCESS ∨ ⌊err⌋ ) ∧ # buf = # buf0 ∧ (err = ESUCCESS → abs-padding(buf)))
Proof step 28:
# lpt1 = # avol, # lpt0 = # avol, EB_PAGE_SIZE = n0 + # buf0 % EB_PAGE_SIZE, lpt1[n] = mklp(m3, # buf0, lpf, m4), avol[n] = mapped(buf0), buf = mkbuf(n0), buf = buf, buf1 = buf, keyset(gch) = gc-heap(lpt1, log0), n < # avol, 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), is-aligned(# buf, 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, # buf ≥ 2 * NODE_HEADER_SIZE ⊦ [persistence_encode_padding_node#(; buf; err)] ( (err = ESUCCESS ∨ ⌊err⌋ ) ∧ # buf = # buf1 ∧ (err = ESUCCESS → abs-padding(buf)) → ⟪isbuf1 := false; bleb1 := buffered(n); if err = ESUCCESS then {awbuf_write_buf#(# buf, buf, adr, m2, log0, lpt0, ns, bleb1; avol, isbuf1; err); m := EB_PAGE_SIZE - lpt1[bleb1.leb].size % EB_PAGE_SIZE; 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)}} else {debug#("persistence: could not encode padding node"); 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)), lpf = LP_FREE, is-aligned(# buf0, EB_PAGE_SIZE)

Rule argument

spec: <toplevel> name: prepost-encode-padding seq: buf0 = buf, is-aligned(# buf, 2 * NODE_HEADER_SIZE), # buf ≥ 2 * NODE_HEADER_SIZE ⊦ ⟪persistence_encode_padding_node#(; buf; err)⟫ ( (err = ESUCCESS ∨ ⌊err⌋ ) ∧ # buf = # buf0 ∧ (err = ESUCCESS → abs-padding(buf))) subst: [buf, err, buf0] → [buf, err, buf] flags: <all paths>

Additional information

Used simplifier rules: flush-padding-space-aligned: ⊦ EB_PAGE_SIZE = n + m % EB_PAGE_SIZE ∧ is-aligned(m, 2 * NODE_HEADER_SIZE) → is-aligned(n, 2 * NODE_HEADER_SIZE);%flush-padding-space-header: ⊦ EB_PAGE_SIZE = n + m % EB_PAGE_SIZE ∧ is-aligned(m, 2 * NODE_HEADER_SIZE) ∧ ¬ is-aligned(m, EB_PAGE_SIZE) → (2 * NODE_HEADER_SIZE ≤ n ↔ n ≠ 0);% ⊦ # mkbuf(n) = n; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult%mult-c: ⊦ m * n = n * m; from specification nat-mult% ⊦ n ≥ m ↔ m ≤ n; (s)% ⊦ n + 0 = n; (s)% ⊦ EB_PAGE_SIZE ≠ 0; (s)%n ≠ 0 ⊦ m % n ≠ n; (s)