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Proof step 51 from proof refine-sync (previous step)

# indx = # lax, # lpt = # avol, # lpt0 = # avol, avol[m2] = mapped(buf), lpt[m2] = mklp(m, # buf, LP_INDEX_NODES, m1), istore[m2] = indexblock(indx, lax, m), keyset(gch) = gc-heap(lpt, log1), remove-refsize0(gstore0) = gstore0, remove-refsize0(istore0) = istore0, elems log1 ∩ ginval = ∅, dom gstore0 ∪ elems log1 = dom gstore ∪ ginval, ginval < # avol, m2 < # avol, abs-gstore(avol, lpt, gstore, ginval), abs-nodes(buf, indx, lax, # buf = LEB_SIZE), awbuf-inv(avol, buffered(m2)), bin-heap-inv(gch, lpt), flash-lpt-cons(lpt0, istore0, gstore0), freelist-cons(lpt, freelist), inv(indexblock(indx, lax, m)), inv(gstore \ ginval), inv(gstore0), inv(istore), inv(istore0), log-group-block(log1, lpt), lpt-free-unref(lpt), lpt-free-unref(lpt0), lpt-leb-size(lpt), lpt-leb-size(lpt0), lpt-ram-flash(lpt, lpt0, log1), m2 ∈ istore, # buf ≤ LEB_SIZE, istore0 ⊑ istore, isbuf → synced(avol) ⊦ dups(log1), is-aligned(# buf, 2 * NODE_HEADER_SIZE)

User applied rule cut formula

And closed the goal!

Rule argument

fma: # buf = LEB_SIZE

Additional information

Used simplifier rules: ⊦ m ≠ n → (m ≤ n ↔ m < n); (s)%⊦ abs-nodes(buf, indx, lax, false) → is-aligned(# buf, 2 * NODE_HEADER_SIZE); (ss)%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult%mult-c: ⊦ m * n = n * m; from specification nat-mult% ⊦ m ≤ m; (s)% ⊦ is-aligned(LEB_SIZE, 2 * NODE_HEADER_SIZE); (ss) Used formulas: # buf = LEB_SIZE