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Proof step 123 from proof inv-format (previous step)

# avol0 = # lpt + 5 + 2 * lptlebs(# lpt, LEB_SIZE), # avol = # avol0, # lebs(avol0, 5, lptlebs(# lpt, LEB_SIZE)) = lptsize(# lpt, LEB_SIZE), avol[0] = mapped(buf), avol0[4] = fill(mkavolume(# avol0), unmapped)[4], avol0[3] = mapped(mkbuf(0)), avol0[2] = fill(mkavolume(# avol0), unmapped)[2], avol0[1] = mapped(mkbuf(0)), avol0[0] = fill(mkavolume(# avol0), unmapped)[0], ebm-vol-inv(fill(mkavolume(# avol0), unmapped)[1, mapped(mkbuf(0))][3, mapped(mkbuf(0))]), ebm-vol-inv(fill(mkavolume(# avol0), unmapped)), ebm-vol-inv(fill(mkavolume(# avol0), unmapped)[1, mapped(mkbuf(0))]), ebm-vol-inv(avol0), ebm-vol-inv(avol), id○(avol, avol0, 0), is-encoded(mksb(adr, m1, 1, 3, 0, 5, 5 + 2 * lptlebs(# lpt, LEB_SIZE)), buf), is-encoded(lpt, lebs(avol0, 5, lptlebs(# lpt, LEB_SIZE))), mapped-full?(avol0, 5, lptlebs(# lpt, LEB_SIZE)), range= (avol0, 5 + lptlebs(# lpt, LEB_SIZE), fill(mkavolume(# avol0), unmapped), 5 + lptlebs(# lpt, LEB_SIZE), lptlebs(# lpt, LEB_SIZE) + # lpt), 5 + 2 * lptlebs(# lpt, LEB_SIZE) ≤ # avol0, 5 ≤ # avol0, 5 + lptlebs(# lpt, LEB_SIZE) ≤ # avol0 ⊦ (∃ lpt0, log, orphans. 2 * lptlebs(# lpt, LEB_SIZE) = 2 * lptlebs(# lpt0, LEB_SIZE) ∧ (5 + 2 * lptlebs(# lpt, LEB_SIZE)) + # lpt0 = # avol0 ∧ avol[3].mapped? ∧ is-encoded-pad(orphans, 0, avol[3].data) ∧ avol[1].mapped? ∧ is-encoded(log, avol[1].data) ∧ mapped-full?(avol0, 5, lptlebs(# lpt0, LEB_SIZE)) ∧ is-encoded(lpt0, lebs(avol, 5, lptlebs(# lpt0, LEB_SIZE)))) ∧ subarray(fill(mkavolume(# avol0), unmapped), 5 + 2 * lptlebs(# lpt, LEB_SIZE), # lpt) = fill(mkavolume(# lpt), unmapped) ∧ avol[1].data = mkbuf(0) ∧ avol[3].data = mkbuf(0), avol[1] = mapped(mkbuf(0)) ∧ avol[3] = mapped(mkbuf(0))

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: array-copy, inst: avolume name: idexcept-extract-left seq: ⊦ avol[n] = aleb → (id○(avol, avol0, n) ↔ avol = avol0[n, aleb]) subst: [aleb, n, avol0, avol] → [mapped(buf), 0, avol0, avol] flags: <all paths>

Additional information

Used simplifier rules: nat-stuff2: ⊦ n = 5 + n1 → n ≠ 0;% ⊦ 0 < m ↔ m ≠ 0; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic%m < # avol ⊦ avol[m, aleb][m] = aleb; (s)% ⊦ mapped(buf) = mapped(buf0) ↔ buf = buf0; (s)% ⊦ # avol[n, aleb] = # avol; (s)%m ≠ n ⊦ avol[(* m), aleb][(* n)] = avol[n]; (s) Used terms: mapped(buf), 0, avol0, avol