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Proof step 9 from proof recovery (previous step)

# lpt0 = # avol0 - m5, m5 + # lpt = # avol0, avol0[m0] = mapped(buf1), avol0[m2] = mapped(buf0), avol0[0] = mapped(buf), disk-layout(mksb(adr, m, m0, m2, m3, m4, m5), # lpt), ebm-vol-inv(avol0), ebm-vol-inv(subarray(avol0, m5, # lpt0)), is-encoded(lpt, lebs(avol0, m4, lptlebs(# lpt, LEB_SIZE))), is-encoded(mksb(adr, m, m0, m2, m3, m4, m5), buf), is-encoded(lpt0, lebs(avol0, m4, lptlebs(# lpt0, LEB_SIZE))), is-encoded(log0, buf1), is-encoded-pad(ns0, m3, buf0), mapped-full?(avol0, m4, lptlebs(# lpt, LEB_SIZE)), avol0 ⊆ avol1, m1 ≠ LEB_SIZE → # buf1 = m1 ⊦ ∃ lpt1. m5 + # lpt1 = # avol0 ∧ mapped-full?(avol0, m4, lptlebs(# lpt1, LEB_SIZE)) ∧ is-encoded(lpt1, lebs(avol0, m4, lptlebs(# lpt1, LEB_SIZE)))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 10:
# lpt0 = n0, # avol0 = n0 + m5, m5 + # lpt = # avol0, avol0[0] = mapped(buf), avol0[m2] = mapped(buf0), avol0[m0] = mapped(buf1), disk-layout(mksb(adr, m, m0, m2, m3, m4, m5), # lpt), ebm-vol-inv(subarray(avol0, m5, # lpt0)), ebm-vol-inv(avol0), is-encoded(log0, buf1), is-encoded(lpt0, lebs(avol0, m4, lptlebs(# lpt0, LEB_SIZE))), is-encoded(mksb(adr, m, m0, m2, m3, m4, m5), buf), is-encoded(lpt, lebs(avol0, m4, lptlebs(# lpt, LEB_SIZE))), is-encoded-pad(ns0, m3, buf0), mapped-full?(avol0, m4, lptlebs(# lpt, LEB_SIZE)), m5 ≤ # avol0, avol0 ⊆ avol1, m1 ≠ LEB_SIZE → # buf1 = m1 ⊦ ∃ lpt1. m5 + # lpt1 = # avol0 ∧ mapped-full?(avol0, m4, lptlebs(# lpt1, LEB_SIZE)) ∧ is-encoded(lpt1, lebs(avol0, m4, lptlebs(# lpt1, LEB_SIZE)))

Rule argument

spec: nat name: elim-sub seq: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n subst: [n, m, n0] → [m5, # avol0, n]

Additional information

Used simplifier rules: ⊦ m ≤ n ↔ ¬ n < m; (ss)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic% ⊦ m < n → n ≠ 0; (s)% ⊦ ¬ m + n < m; (s)%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: m5, # avol0, n