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Proof step 206 from proof inv-read-gblock-nodes (previous step)

# gndx = # lax, # lpt = # avol, # lpt0 = # avol, LEB_SIZE = n0 + # buf1, avol[m5] = mapped(buf1), m5 < # avol, abs-nodes(buf1, gndx, lax, true), awbuf-inv(avol, bleb), buf-ro-rw-mode(isbuf, bleb, lpt0, avol), bufs-log-only(bleb, log0, lpt0), lpt-free-unref(lpt), lpt-leb-size(lpt), lpt-ram-flash(lpt0, lpt, log0), read-gblock-inv(m5, m0, ax, gndx0, ax0, gndx1, buf1, true), # buf1 ≤ LEB_SIZE ⊦ ax = ax0 + lax.to-adr(m5) ∧ gndx0 = gndx1 + gndx

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 207:
⊦ read-gblock-inv(m, n, ax, gndx, ax0, gndx0, buf, boolvar) ↔ (∃ gndx1, gndx2, lax1, lax2, buf0, buf1. ax = ax0 + lax1.to-adr(m) ∧ gndx = gndx0 + gndx1 ∧ buf = buf0 + buf1 ∧ # buf0 = n ∧ abs-nodes(buf0, gndx1, lax1, false) ∧ abs-nodes(buf1, # buf0, gndx2, lax2, true) ∧ (boolvar → gndx2 = [] ∧ lax2 = []))

Rule argument

spec: persistence-base name: read-gblock-inv seq: ⊦ read-gblock-inv(m, n, ax, gndx, ax0, gndx0, buf, boolvar) ↔ (∃ gndx1, gndx2, lax1, lax2, buf0, buf1. ax = ax0 + lax1.to-adr(m) ∧ gndx = gndx0 + gndx1 ∧ buf = buf0 + buf1 ∧ # buf0 = n ∧ abs-nodes(buf0, gndx1, lax1, false) ∧ abs-nodes(buf1, # buf0, gndx2, lax2, true) ∧ (boolvar → gndx2 = [] ∧ lax2 = [])) subst: [boolvar, buf, gndx0, ax0, gndx, ax, n, m] → [true, buf1, gndx1, ax0, gndx0, ax, m0, m5] flags: <all paths>

Additional information

Used simplifier rules: ⊦ #(buf + buf0) = # buf + # buf0; (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%⊦ abs-nodes(buf0, gndx, lax0, false) → ( abs-nodes(buf0 + buf1, gndx0, lax1, boolvar1) ↔ (∃ gndx1, lax2. gndx0 = gndx + gndx1 ∧ lax1 = lax0 + lax2 ∧ abs-nodes(buf1, # buf0, gndx1, lax2, boolvar1))); (s)%⊦ abs-nodes(buf, m, gndx, lax0, true) → (abs-nodes(buf, m, gndx0, lax1, true) ↔ gndx = gndx0 ∧ lax0 = lax1); (s)% ⊦ ax + ax0 = ax + ax1 ↔ ax0 = ax1; (s)% ⊦ lax0.to-adr(n) = lax1.to-adr(n) ↔ lax0 = lax1; (s)%a: ⊦ (ax + ax0) + ax1 = ax + ax0 + ax1; from specification list[address-list-set]% ⊦ gndx + gndx0 = gndx + gndx1 ↔ gndx0 = gndx1; (s)%a: ⊦ (gndx + gndx0) + gndx1 = gndx + gndx0 + gndx1; from specification list[group-store]%abs-nodes-elems-adr-length-h: ⊦ abs-nodes(buf, m, gndx, lax, weak) → # gndx = # lax; (forward) from specification abs-list[encoding-group-node]%abs-nodes-elems-adr-length: ⊦ abs-nodes(buf, gndx, lax, weak) → # gndx = # lax; (forward) from specification abs-list[encoding-group-node]% ⊦ # [] = 0; (s)% ⊦ # [] = 0; (s)% ⊦ gndx + [] = gndx; (s)% ⊦ lax + [] = lax; (s)%a: ⊦ (lax + lax0) + lax1 = lax + lax0 + lax1; from specification list[laddress-list] Used terms: true, buf1, gndx1, ax0, gndx0, ax, m0, m5