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Proof step 77 from proof refine-remap (previous step)

# avol0 = # avol1, # lpt0 = # avol1, # buf = EB_PAGE_SIZE, avol0[m] = mapped(buf0), bleb0 = buffered(m), m < # avol1, m4 < # avol1, abs(avol1, bleb0, mkwbuf(buf, m3, m2), avol0, rofs), awbuf-inv(avol1, bleb0), ebm-vol-inv(avol0), synced(avol1), wbuf-cons(mkwbuf(buf, m3, m2), mapped(buf0), rofs), ⌊err1⌋ ⊦ bleb0 = nobuffer, buffered(m4) = bleb0, abs(avol1[m4, unmapped], bleb0, mkwbuf(buf, m3, m2), avol0[m4, unmapped], rofs), abs(avol1, bleb0, mkwbuf(buf, m3, m2), avol0[m4, unmapped], rofs)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 78:
# avol0 = # avol1, # lpt0 = # avol1, # buf = EB_PAGE_SIZE, avol0[m] = mapped(buf0), m < # avol1, m4 < # avol1, abs(avol1, buffered(m), mkwbuf(buf, m3, m2), avol0, rofs), awbuf-inv(avol1, buffered(m)), ebm-vol-inv(avol0), synced(avol1), wbuf-cons(mkwbuf(buf, m3, m2), mapped(buf0), rofs), ⌊err1⌋ ⊦ m4 = m, abs(avol1[m4, unmapped], buffered(m), mkwbuf(buf, m3, m2), avol0[m4, unmapped], rofs), abs(avol1, buffered(m), mkwbuf(buf, m3, m2), avol0[m4, unmapped], rofs)

Rule argument

Additional information

Used simplifier rules: inv-buf-in-vol: ⊦ awbuf-inv(avol, buffered(n)) → n < # avol; (forward) from specification awbuf-inv%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic% ⊦ nobuffer ≠ buffered(m); (s)% ⊦ buffered(m) = buffered(m0) ↔ m = m0; (s)