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Proof step 8 from proof inv-remap (previous step)

m5 + # lpt = # avol, avol[m1] = mapped(buf1), avol[m2] = mapped(buf0), avol[0] = mapped(buf), m < # lpt, disk-layout(mksb(adr, m0, m1, m2, m3, m4, m5), # lpt), ebm-vol-inv(avol), is-encoded(mksb(adr, m0, m1, m2, m3, m4, m5), buf), is-encoded(lpt, lebs(avol, m4, lptlebs(# lpt, LEB_SIZE))), is-encoded(log, buf1), is-encoded-pad(orphans, m3, buf0), mapped-full?(avol, m4, lptlebs(# lpt, LEB_SIZE)), logoff ≠ LEB_SIZE → # buf1 = logoff ⊦ ⟪ebm_avol_remap#(m5 + m; avol; err)⟫ ( (∃ lpt0, log, orphans. disk-layout(mksb(adr, m0, m1, m2, m3, m4, m5), # lpt0) ∧ m5 + # lpt0 = # avol ∧ avol[0].mapped? ∧ is-encoded(mksb(adr, m0, m1, m2, m3, m4, m5), avol[0].data) ∧ avol[m2].mapped? ∧ is-encoded-pad(orphans, m3, avol[m2].data) ∧ avol[m1].mapped? ∧ (logoff ≠ LEB_SIZE → # avol[m1].data = logoff) ∧ is-encoded(log, avol[m1].data) ∧ mapped-full?(avol, m4, lptlebs(# lpt0, LEB_SIZE)) ∧ is-encoded(lpt0, lebs(avol, m4, lptlebs(# lpt0, LEB_SIZE)))) ∧ ebm-vol-inv(avol))

User applied rule insert program lemma

And obtained the following new goals

Proof step 9:
ebm-vol-inv(avol), m < # avol ⊦ ⟪ebm_avol_remap#(m; avol; err)⟫ ebm-vol-inv(avol)
Proof step 10:
m5 + # lpt = # avol, avol[0] = mapped(buf), avol[m2] = mapped(buf0), avol[m1] = mapped(buf1), m6 = m5 + m, m < # lpt, m5 + m < # avol, disk-layout(mksb(adr, m0, m1, m2, m3, m4, m5), # lpt), ebm-vol-inv(avol), is-encoded(log, buf1), is-encoded(lpt, lebs(avol, m4, lptlebs(# lpt, LEB_SIZE))), is-encoded(mksb(adr, m0, m1, m2, m3, m4, m5), buf), is-encoded-pad(orphans, m3, buf0), mapped-full?(avol, m4, lptlebs(# lpt, LEB_SIZE)), logoff ≠ LEB_SIZE → # buf1 = logoff ⊦ [ebm_avol_remap#(m5 + m; avol; err)] ( ebm-vol-inv(avol) → (∃ lpt0, log, orphans. disk-layout(mksb(adr, m0, m1, m2, m3, m4, m5), # lpt0) ∧ m5 + # lpt0 = # avol ∧ avol[0].mapped? ∧ is-encoded(mksb(adr, m0, m1, m2, m3, m4, m5), avol[0].data) ∧ avol[m2].mapped? ∧ is-encoded-pad(orphans, m3, avol[m2].data) ∧ avol[m1].mapped? ∧ (logoff ≠ LEB_SIZE → # avol[m1].data = logoff) ∧ is-encoded(log, avol[m1].data) ∧ mapped-full?(avol, m4, lptlebs(# lpt0, LEB_SIZE)) ∧ is-encoded(lpt0, lebs(avol, m4, lptlebs(# lpt0, LEB_SIZE)))) ∧ ebm-vol-inv(avol))

Rule argument

spec: ebm-avol-asm name: inv-remap seq: ebm-vol-inv(avol), m < # avol ⊦ ⟪ebm_avol_remap#(m; avol; err)⟫ ebm-vol-inv(avol) subst: [m, avol, err] → [m5 + m, avol, err] flags: <all paths>

Additional information

Used simplifier rules: a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ m = m0 + n0 ∧ n < n0 → m0 + n < m; (s)