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Proof step 41 from proof prepost-replay-lpt (previous step)

# avol1 = n2 + n0, # lpt4 = n2 + n0, # avol = n2 + n0, lpt4[n0] = mklp(0, m1, lpf, m2), avol-replay-lpt-unchanged(avol1, avol, lpt4, log0), awbuf-inv(avol, nobuffer), awbuf-inv(avol1, nobuffer), synced(avol), synced(avol1) ⊦ lpf = LP_FREE, lpf = LP_INDEX_NODES, n2 = 0, n0 ∈ log0, awbuf-inv(avol[n0, unmapped], nobuffer) ∧ avol-replay-lpt-unchanged(avol1, avol[n0, unmapped], lpt4, log0)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: awbuf-inv name: inv-unmap seq: ⊦ bleb ≠ buffered(n) ∧ awbuf-inv(avol, bleb) → awbuf-inv(avol[n, unmapped], bleb) subst: [bleb, n, avol] → [nobuffer, n0, avol] flags: <all paths>

Additional information

Used simplifier rules: ⊦ nobuffer ≠ buffered(m); (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ m + m0 ≤ m ↔ m0 = 0; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic%n < # avol1 ⊦ avol-replay-lpt-unchanged(avol0, avol1, lpt, nx) → ( avol-replay-lpt-unchanged(avol0, avol1[n, aleb], lpt, nx) ↔ ¬ ( aleb ≠ avol0[n] ∧ (n ∈ nx ∨ lpt[n].ref-size ≠ 0 ∨ lpt[n].flags = LP_FREE))); (ss)% ⊦ mklp(n2, n3, lpf, m).ref-size = n2; (s)% ⊦ mklp(n2, n3, lpf, m).flags = lpf; (s) Used terms: nobuffer, n0, avol