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Proof step 15 from proof abs-nodes-inv-flashsize-h (previous step)

# gndx0 = # lax0, abs-nodes(buf0, m + # buf1, gnd ' + gndx0, @(m0, m1) ' + lax0, weak), abs-padding(buf1), ∀ buf2, m, gndx, lax, weak. # buf2 < #(buf1 + buf0) → abs-nodes(buf2, m, gndx, lax, weak) → inv-flashsize(gndx, lax) ⊦ 2 * NODE_HEADER_SIZE + gnd.alignedsize = m1 ∧ inv-flashsize(gndx0, lax0)

User applied rule apply induction

And closed the goal!

Rule argument

subst: [buf2, m, gndx, lax, weak] → [buf0, m + # buf1, gnd ' + gndx0, @(m0, m1) ' + lax0, weak]

Additional information

Used simplifier rules: ⊦ inv-flashsize(gnd ' + gndx, ladr ' + lax) ↔ gnd.flashsize = ladr.size ∧ inv-flashsize(gndx, lax); (s)% ⊦ gnd.flashsize = 2 * NODE_HEADER_SIZE + gnd.alignedsize; (s)% ⊦ @(m, m0).size = m0; (s)%a: ⊦ (lax + lax0) + lax1 = lax + lax0 + lax1; from specification list[laddress-list]%a: ⊦ (gndx + gndx0) + gndx1 = gndx + gndx0 + gndx1; from specification list[group-store]% ⊦ #(buf + buf0) = # buf + # buf0; (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ m + m0 ≤ m ↔ m0 = 0; (s)% ⊦ # buf = 0 ↔ buf = mkbuf(0); (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ # mkbuf(n) = n; (s)% ⊦ n + 0 = n; (s)% ⊦ ¬ abs-padding(mkbuf(0)); (s) Used terms: buf0, m + # buf1, gnd ' + gndx0, @(m0, m1) ' + lax0, weak