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Proof step 78 from proof refine-sync (previous step)

# lpt0 = # avol, # lpt1 = # avol, EB_PAGE_SIZE = n0 + # buf0 % EB_PAGE_SIZE, lpt1[pstate.lnum] = mklp(m1, # buf0, lpf, m4), avol[pstate.lnum] = mapped(buf0), buf = mkbuf(n0), keyset(gch) = gc-heap(lpt1, log1), remove-refsize0(gstore0) = gstore0, remove-refsize0(istore0) = istore0, elems log1 ∩ ginval = ∅, dom gstore0 ∪ elems log1 = dom gstore ∪ ginval, lpf ≠ LP_FREE, pstate ≠ unbuffered, pstate ≠ readonly, ginval < # avol, pstate.lnum < # avol, abs-gstore(avol, lpt1, gstore, ginval), abs-istore(avol, lpt1, istore), awbuf-inv(avol, buffered(pstate.lnum)), bin-heap-inv(gch, lpt1), buf-ro-rw-mode(false, buffered(pstate.lnum), lpt1, avol), bufs-log-only(buffered(pstate.lnum), log1, lpt1), flash-lpt-cons(lpt0, istore0, gstore0), freelist-cons(lpt1, freelist), inv(gstore \ ginval), inv(gstore0), inv(istore), inv(istore0), is-aligned(# buf0, 2 * NODE_HEADER_SIZE), log-group-block(log1, lpt1), lpt-free-unref(lpt0), lpt-free-unref(lpt1), lpt-leb-size(lpt0), lpt-leb-size(lpt1), lpt-ram-flash(lpt1, lpt0, log1), # buf0 ≤ LEB_SIZE, istore0 ⊑ istore, ¬ dups(log1), ¬ is-aligned(# buf0, EB_PAGE_SIZE), pstate.journal? → log1 ≠ [] ∧ pstate.lnum = log1.last ∧ pstate.lnum ∈ gstore, pstate.index? → pstate.lnum ∈ istore ⊦ [persistence_encode_padding_node#(; buf; err); isbuf2 := pstate = readonly; bleb1 := buffered(pstate.lnum); if err = ESUCCESS then {awbuf_write_buf#(# buf, buf, adr0, m, log1, lpt0, ns0, bleb1; avol, isbuf2; err); m0 := lpt1[bleb1.leb].size; if err = ESUCCESS then lpt1[bleb1.leb] := mklp (lpt1[bleb1.leb].ref-size, lpt1[bleb1.leb].size + (EB_PAGE_SIZE - m0 % EB_PAGE_SIZE), 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#(adr0, m, log1, avol, lpt0, ns0, bleb1; ; isbuf2)}} else {debug#("persistence: could not encode padding node"); awbuf_enter_readonly#(adr0, m, log1, avol, lpt0, ns0, bleb1; ; isbuf2)}] ( lpt-free-unref(lpt1) ∧ freelist-cons(lpt1, freelist) ∧ bin-heap-inv(gch, lpt1) ∧ keyset(gch) = gc-heap(lpt1, log1) ∧ bufs-log-only(bleb1, log1, lpt1) ∧ # lpt1 = # avol ∧ log-group-block(log1, lpt1) ∧ buf-ro-rw-mode(isbuf2, bleb1, lpt1, avol) ∧ lpt-leb-size(lpt1) ∧ lpt-ram-flash(lpt1, lpt0, log1) ∧ awbuf-inv(avol, bleb1) ∧ # lpt0 = # avol → ⟨isbuf1 := false; apersistence_sync#(adr0, istore, istore0, ginval, gstore, gstore0, log1, m, ns0; pstate, isbuf1; err0)⟩ ( abs-istore(avol, lpt1, istore) ∧ abs-gstore(avol, lpt1, gstore, ginval) ∧ ginval < # lpt1 ∧ (isbuf1 → synced(avol)) ∧ (pstate = unbuffered → bleb1 = nobuffer) ∧ (pstate = readonly ↔ isbuf2) ∧ (pstate ≠ unbuffered ∧ pstate ≠ readonly → bleb1 = buffered(pstate.lnum)) ∧ err = err0))

User applied rule insert program lemma

And obtained the following new goals

Rule argument

spec: persistence-asm 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: List([[1,0,0]])

Additional information

Used simplifier rules: ⊦ # 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%⊦ EB_PAGE_SIZE = n + m % EB_PAGE_SIZE ∧ is-aligned(m, 2 * NODE_HEADER_SIZE) → is-aligned(n, 2 * NODE_HEADER_SIZE); (s)% ⊦ n ≥ m ↔ m ≤ n; (s)%⊦ 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); (s)% ⊦ n + 0 = n; (s)% ⊦ EB_PAGE_SIZE ≠ 0; (s)%n ≠ 0 ⊦ m % n ≠ n; (s)