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Proof step 21 from proof prepost-encode-group-nodes (previous step)

# gndx0 = # lax, # buf0 = gndx0.flashsize, # buf1 = gndx1.flashsize, buf = buf0 + buf1, buf = buf, buf2 = buf, gnd0 = (gndx0 + gndx1)[# lax], n0 = gndx0.flashsize, abs-nodes(buf0, n, gndx0, lax, false), gndx0.flashsize + (gndx0 + gndx1)[# lax].flashsize ≤ # buf ⊦ [encode_group_node#((gndx0 + gndx1)[# lax], gndx0.flashsize; m3, buf; err)] ( (err = ESUCCESS ∨ ⌊err⌋ ) ∧ # buf = # buf2 ∧ subarray(buf, 0, n0) = subarray(buf2, 0, n0) ∧ subarray(buf, n0 + gnd0.flashsize, # buf2 - n0 + gnd0.flashsize) = subarray(buf2, n0 + gnd0.flashsize, # buf2 - n0 + gnd0.flashsize) ∧ (err = ESUCCESS → abs-node(subarray(buf, n0, gnd0.flashsize), gnd0) ∧ m3 = gnd0.flashsize) → ⟪ax := lax.to-adr(m2) + @(m2, n + gndx0.flashsize, m3) '; m0 := gndx0.flashsize + m3; m1 := # gndx0 + 1⟫ ( m1 ≤ # gndx0 + # gndx1 ∧ (err = ESUCCESS ∨ ⌊err⌋ ) ∧ ( err = ESUCCESS → # buf = gndx0.flashsize + gndx1.flashsize ∧ (∃ gndx2, gndx3. gndx0 + gndx1 = gndx2 + gndx3 ∧ # gndx2 = m1 ∧ m0 = gndx2.flashsize ∧ (∃ lax, buf0, buf1. lax.to-adr(m2) = ax ∧ buf = buf0 + buf1 ∧ # buf0 = gndx2.flashsize ∧ abs-nodes(buf0, n, gndx2, lax, false)))) ∧ # gndx0 + # gndx1 - m1 < # gndx1)), # lax + # gndx1 = 0, gndx1 = []

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 22:
# gndx0 = # lax, # buf0 = gndx0.flashsize, # buf1 = gndx1.flashsize, buf = buf0 + buf1, # lax + # gndx1 ≠ 0, gndx1 ≠ [], abs-nodes(buf0, n, gndx0, lax, false), 2 * NODE_HEADER_SIZE + (gndx0 + gndx1)[# lax].alignedsize ≤ gndx1.flashsize ⊦ [encode_group_node#((gndx0 + gndx1)[# lax], gndx0.flashsize; m3, buf; err)] ( (err = ESUCCESS ∨ ⌊err⌋ ) ∧ # buf = gndx0.flashsize + # buf1 ∧ subarray(buf, 0, gndx0.flashsize) = buf0 ∧ subarray (buf, gndx0.flashsize + 2 * NODE_HEADER_SIZE + (gndx0 + gndx1)[# lax].alignedsize, # buf1 - 2 * NODE_HEADER_SIZE + (gndx0 + gndx1)[# lax].alignedsize) = subarray (buf1, 2 * NODE_HEADER_SIZE + (gndx0 + gndx1)[# lax].alignedsize, # buf1 - 2 * NODE_HEADER_SIZE + (gndx0 + gndx1)[# lax].alignedsize) ∧ ( err = ESUCCESS → abs-node(subarray(buf, gndx0.flashsize, 2 * NODE_HEADER_SIZE + (gndx0 + gndx1)[# lax].alignedsize), (gndx0 + gndx1)[# lax]) ∧ m3 = 2 * NODE_HEADER_SIZE + (gndx0 + gndx1)[# lax].alignedsize) → ⟪ax := lax.to-adr(m2) + @(m2, n + gndx0.flashsize, m3) '; m0 := gndx0.flashsize + m3; m1 := # gndx0 + 1⟫ ( m1 ≤ # gndx0 + # gndx1 ∧ (err = ESUCCESS ∨ ⌊err⌋ ) ∧ ( err = ESUCCESS → # buf = gndx0.flashsize + gndx1.flashsize ∧ (∃ gndx2, gndx3. gndx0 + gndx1 = gndx2 + gndx3 ∧ # gndx2 = m1 ∧ m0 = gndx2.flashsize ∧ (∃ lax, buf0, buf1. lax.to-adr(m2) = ax ∧ buf = buf0 + buf1 ∧ # buf0 = gndx2.flashsize ∧ abs-nodes(buf0, n, gndx2, lax, false)))) ∧ # gndx0 + # gndx1 - m1 < # gndx1))

Rule argument

Additional information

Used simplifier rules: ⊦ m + n - m = n; (s)%# buf ≤ n0, n0 + m ≤ # buf + # buf0 ⊦ subarray(buf + buf0, n0, m) = subarray(buf0, n0 - # buf, m); (s)% ⊦ m ≤ m; (s)% ⊦ n ≤ n0 → (m + (n0 - n)) + n = m + n0; (s)% ⊦ m ≤ m + n; (s)% ⊦ m + n - n + n1 = m - n1; (s)% ⊦ # subarray(buf, m, n) = n; (s)%n = # buf ⊦ subarray(buf + buf0, 0, n) = buf; (s)%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ m + n ≤ m + n0 ↔ n ≤ n0; (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]% ⊦ #(buf + buf0) = # buf + # buf0; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ gnd.flashsize = 2 * NODE_HEADER_SIZE + gnd.alignedsize; (s)