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Proof step 44 from proof prepost-encode-group-nodes (previous step)

# buf = 2 * NODE_HEADER_SIZE + gnd.alignedsize, # buf0 = gndx3.flashsize, # gndx0 = # lax, subarray(buf2, gndx0.flashsize + # buf, gndx3.flashsize) = subarray(buf0 + buf, # buf, gndx3.flashsize), abs-node(subarray(buf2, gndx0.flashsize, # buf), gnd), abs-nodes(subarray(buf2, 0, gndx0.flashsize), n, gndx0, lax, false), ∃ buf0, buf1. buf2 = buf0 + buf1 ∧ # buf0 = gndx0.flashsize ∧ # buf1 = gndx3.flashsize + # buf ⊦ ∃ buf, buf0. buf2 = buf + buf0 ∧ # buf = gndx0.flashsize + 2 * NODE_HEADER_SIZE + gnd.alignedsize ∧ abs-nodes(buf, n, gndx0 + gnd ', lax + @(n + gndx0.flashsize, 2 * NODE_HEADER_SIZE + gnd.alignedsize) ', false)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 45:
# buf1 = gndx3.flashsize + # buf, # buf3 = gndx0.flashsize, # buf = 2 * NODE_HEADER_SIZE + gnd.alignedsize, # buf0 = gndx3.flashsize, # gndx0 = # lax, subarray(buf1, # buf, gndx3.flashsize) = subarray(buf0 + buf, # buf, gndx3.flashsize), abs-node(subarray(buf1, 0, # buf), gnd), abs-nodes(buf3, n, gndx0, lax, false) ⊦ ∃ buf, buf0. buf3 + buf1 = buf + buf0 ∧ # buf = gndx0.flashsize + 2 * NODE_HEADER_SIZE + gnd.alignedsize ∧ abs-nodes(buf, n, gndx0 + gnd ', lax + @(n + gndx0.flashsize, 2 * NODE_HEADER_SIZE + gnd.alignedsize) ', false)

Rule argument

Additional information

Used simplifier rules: ⊦ m - m = 0; (s)% ⊦ m + n - m = n; (s)% ⊦ ¬ m + n < m; (s)% ⊦ # buf = 0 ↔ buf = mkbuf(0); (s)% ⊦ m ≤ m; (s)%# buf ≤ n0, n0 + m ≤ # buf + # buf0 ⊦ subarray(buf + buf0, n0, m) = subarray(buf0, n0 - # buf, m); (s)% ⊦ ¬ n < n; (s)% ⊦ m + n < m + n0 ↔ n < n0; (s)% ⊦ m < n → n ≠ 0; (s)%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ m ≤ n ↔ ¬ n < m; (ss)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]%n = # buf ⊦ subarray(buf + buf0, 0, n) = buf; (s)% ⊦ m + n ≤ m + n0 ↔ n ≤ n0; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m ≤ m + n; (s)