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Proof step 144 from proof inv-read-gblock-nodes (previous step)

# gndx = # lax, # lpt = # avol, # lpt0 = # avol, LEB_SIZE = n0 + # buf1, avol[m5] = mapped(buf1), align↑(m2, 2 * NODE_HEADER_SIZE) = gnd.alignedsize, m5 < # avol, m1 < LEB_SIZE, abs-node(subarray(buf1 + mkempbuf(n0), m1, 2 * NODE_HEADER_SIZE + gnd.alignedsize), gnd), abs-nodes(buf1, gndx, lax, true), awbuf-inv(avol, bleb), buf-ro-rw-mode(isbuf, bleb, lpt0, avol), bufs-log-only(bleb, log0, lpt0), is-encoded(nodeheader(m2, false), subarray(buf1 + mkempbuf(n0), m1, NODE_HEADER_SIZE)), lpt-free-unref(lpt), lpt-leb-size(lpt), lpt-ram-flash(lpt0, lpt, log0), range=(buf1 + mkempbuf(n0), m1 + NODE_HEADER_SIZE + gnd.alignedsize, validtrailer, 0, NODE_HEADER_SIZE), read-gblock-inv(m5, m1, ax0, gndx0, ax1, gndx2, buf1, false), m1 + NODE_HEADER_SIZE ≤ LEB_SIZE, # buf1 ≤ LEB_SIZE, m1 + 2 * NODE_HEADER_SIZE + gnd.alignedsize ≤ LEB_SIZE ⊦ isempty(buf1 + mkempbuf(n0), m1, NODE_HEADER_SIZE), read-gblock-inv (m5, m1 + 2 * NODE_HEADER_SIZE + gnd.alignedsize, ax0 + @(m5, m1, 2 * NODE_HEADER_SIZE + gnd.alignedsize) ', gndx0 + gnd ', ax1, gndx2, buf1, false) ∧ (LEB_SIZE - m1 + 2 * NODE_HEADER_SIZE + gnd.alignedsize) + m1 < LEB_SIZE

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 145:
# lpt0 = # avol, # lpt = # avol, # gndx = # lax, LEB_SIZE = n0 + # buf1, LEB_SIZE = n1 + m1 + 2 * NODE_HEADER_SIZE + gnd.alignedsize, avol[m5] = mapped(buf1), align↑(m2, 2 * NODE_HEADER_SIZE) = gnd.alignedsize, m1 < LEB_SIZE, m5 < # avol, abs-node(subarray(buf1 + mkempbuf(n0), m1, 2 * NODE_HEADER_SIZE + gnd.alignedsize), gnd), abs-nodes(buf1, gndx, lax, true), awbuf-inv(avol, bleb), buf-ro-rw-mode(isbuf, bleb, lpt0, avol), bufs-log-only(bleb, log0, lpt0), is-encoded(nodeheader(m2, false), subarray(buf1 + mkempbuf(n0), m1, NODE_HEADER_SIZE)), lpt-free-unref(lpt), lpt-leb-size(lpt), lpt-ram-flash(lpt0, lpt, log0), range=(buf1 + mkempbuf(n0), m1 + NODE_HEADER_SIZE + gnd.alignedsize, validtrailer, 0, NODE_HEADER_SIZE), read-gblock-inv(m5, m1, ax0, gndx0, ax1, gndx2, buf1, false), m1 + 2 * NODE_HEADER_SIZE + gnd.alignedsize ≤ LEB_SIZE, # buf1 ≤ LEB_SIZE, m1 + NODE_HEADER_SIZE ≤ LEB_SIZE ⊦ isempty(buf1 + mkempbuf(n0), m1, NODE_HEADER_SIZE), read-gblock-inv (m5, m1 + 2 * NODE_HEADER_SIZE + gnd.alignedsize, ax0 + @(m5, m1, 2 * NODE_HEADER_SIZE + gnd.alignedsize) ', gndx0 + gnd ', ax1, gndx2, buf1, false) ∧ n1 + m1 < LEB_SIZE

Rule argument

spec: nat name: elim-sub seq: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n subst: [m, n, n0] → [LEB_SIZE, m1 + 2 * NODE_HEADER_SIZE + gnd.alignedsize, n]

Additional information

Used simplifier rules: a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic%n ≤ m ⊦ n0 = m - n ↔ m = n0 + n; (elim) Used terms: LEB_SIZE, m1 + 2 * NODE_HEADER_SIZE + gnd.alignedsize, n