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Proof step 129 from proof refine-allocate-gnd (previous step)

# lpt = # avol0, # lpt0 = # avol0, n < # avol0 ∧ lpf0 = LP_GROUP_NODES ↔ n ∈ gstore, lpt[n] = mklp(m6, m7, lpf0, m8), gstore[n] = groupblock(gndx0, lax0, m5), lpt[n0, mklp(0, 0, LP_GROUP_NODES, m4)][n] = mklp(m0, m2, lpf, m3), gstore[n0, groupblock([], [], 0)][n] = groupblock(gndx, lax, m), lpt[n0] = mklp(0, m1, LP_FREE, m4), keyset(gch) = gc-heap(lpt, log1), remove-refsize0(gstore0) = gstore0, remove-refsize0(istore1) = istore1, elems log1 ∩ ginval = ∅, dom gstore0 ∪ elems log1 = dom gstore ∪ ginval, ginval < # avol0, n0 < # avol0, abs-istore(avol0, lpt, istore2), awbuf-inv(avol0, bleb), bin-heap-inv(gch, lpt), buf-ro-rw-mode(false, bleb, lpt, avol0), bufs-log-only(bleb, log1, lpt), flash-lpt-cons(lpt0, istore1, gstore0), freelist-cons(lpt, n0 ' + nx0), inv(gstore \ ginval), inv(gstore0), inv(istore2), inv(istore1), 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), synced(avol0), istore1 ⊑ istore2, n ∈ gstore → m6 = m5, n ∈ gstore ∧ ¬ n ∈ ginval → abs-leb(avol0[n], groupblock(gndx0, lax0, m5), mklp(m6, m7, lpf0, m8)), pstate = unbuffered → bleb = nobuffer, pstate.journal? → log1 ≠ [] ∧ pstate.lnum = log1.last ∧ pstate.lnum ∈ gstore, pstate.index? → pstate.lnum ∈ istore2, pstate ≠ unbuffered → bleb = buffered(pstate.lnum) ⊦ pstate = readonly, dups(log1), (n < # avol0 ∧ lpf = LP_GROUP_NODES ↔ n ∈ gstore[n0, groupblock([], [], 0)]) ∧ ( n ∈ gstore[n0, groupblock([], [], 0)] ∧ (n = n0 ∨ ¬ n ∈ ginval) → abs-leb(avol0[n0, mapped(mkbuf(0))][n], groupblock(gndx, lax, m), mklp(m0, m2, lpf, m3))) ∧ (n ∈ gstore[n0, groupblock([], [], 0)] → m0 = m)

Heuristic nonsplitting cut applied rule cut formula

And obtained the following new goals

Proof step 130:
# lpt0 = # avol0, # lpt = # avol0, n < # avol0 ∧ lpf0 = LP_GROUP_NODES ↔ n ∈ gstore, lpt[n0] = mklp(0, m1, LP_FREE, m4), gstore[n0, groupblock([], [], 0)][n] = groupblock(gndx, lax, m), lpt[n0, mklp(0, 0, LP_GROUP_NODES, m4)][n] = mklp(m0, m2, lpf, m3), gstore[n] = groupblock(gndx0, lax0, m5), lpt[n] = mklp(m6, m7, lpf0, m8), keyset(gch) = gc-heap(lpt, log1), n = n0, remove-refsize0(istore1) = istore1, remove-refsize0(gstore0) = gstore0, elems log1 ∩ ginval = ∅, dom gstore0 ∪ elems log1 = dom gstore ∪ ginval, n0 < # avol0, ginval < # avol0, abs-istore(avol0, lpt, istore2), awbuf-inv(avol0, bleb), bin-heap-inv(gch, lpt), buf-ro-rw-mode(false, bleb, lpt, avol0), bufs-log-only(bleb, log1, lpt), flash-lpt-cons(lpt0, istore1, gstore0), freelist-cons(lpt, n0 ' + nx0), inv(istore1), inv(istore2), inv(gstore0), inv(gstore \ ginval), log-group-block(log1, lpt), lpt-free-unref(lpt0), lpt-free-unref(lpt), lpt-leb-size(lpt0), lpt-leb-size(lpt), lpt-ram-flash(lpt, lpt0, log1), synced(avol0), istore1 ⊑ istore2, pstate ≠ unbuffered → bleb = buffered(pstate.lnum), pstate.index? → pstate.lnum ∈ istore2, pstate.journal? → log1 ≠ [] ∧ pstate.lnum = log1.last ∧ pstate.lnum ∈ gstore, pstate = unbuffered → bleb = nobuffer, n ∈ gstore ∧ ¬ n ∈ ginval → abs-leb(avol0[n], groupblock(gndx0, lax0, m5), mklp(m6, m7, lpf0, m8)), n ∈ gstore → m6 = m5 ⊦ pstate = readonly, dups(log1), (n < # avol0 ∧ lpf = LP_GROUP_NODES ↔ n ∈ gstore[n0, groupblock([], [], 0)]) ∧ ( n ∈ gstore[n0, groupblock([], [], 0)] ∧ (n = n0 ∨ ¬ n ∈ ginval) → abs-leb(avol0[n0, mapped(mkbuf(0))][n], groupblock(gndx, lax, m), mklp(m0, m2, lpf, m3))) ∧ (n ∈ gstore[n0, groupblock([], [], 0)] → m0 = m)

Rule argument

fma: n = n0

Additional information

Used simplifier rules: ⊦ m ≠ n → lpt[n, lp][m] = lpt[m]; (s)% ⊦ n ≠ n0 → gstore[n0, gblock][n] = gstore[n]; (s)% ⊦ n ≠ n0 → (n ∈ gstore[n0, gblock] ↔ n ∈ gstore); (s)% ⊦ m ≠ n → avol[n, aleb][m] = avol[m]; (s)%⊦ groupblock(gndx, lax, m) = groupblock(gndx0, lax0, m0) ↔ gndx = gndx0 ∧ lax = lax0 ∧ m = m0; (ws)%⊦ mklp(m, m0, lpf, m1) = mklp(m2, m3, lpf0, m4) ↔ m = m2 ∧ m0 = m3 ∧ lpf = lpf0 ∧ m1 = m4; (ws) Used formulas: n = n0