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Proof step 3 from proof abs-nodes-prefix-elim (previous step)

abs-nodes(buf0, 0, x0, lax0, false) ⊦ abs-nodes(buf0 + buf1, 0, x1, lax1, boolvar1) ↔ (∃ x2, lax2. x1 = x0 + x2 ∧ lax1 = lax0 + lax2 ∧ abs-nodes(buf1, # buf0, x2, lax2, boolvar1))

User applied rule case distinction

And obtained the following new goals

Proof step 4:
abs-nodes(buf0, 0, x0, lax0, false), abs-nodes(buf0 + buf1, 0, x1, lax1, boolvar1) ⊦ ∃ x2, lax2. x1 = x0 + x2 ∧ lax1 = lax0 + lax2 ∧ abs-nodes(buf1, # buf0, x2, lax2, boolvar1)

Rule argument

pos: right 1

Additional information

Used simplifier rules: abs-nodes-append-h: ⊦ abs-nodes(buf0, m, x0, lax0, false) → ( abs-nodes(buf0 + buf1, m, x0 + x1, lax0 + lax1, weak) ↔ abs-nodes(buf1, m + # buf0, x1, lax1, weak));%abs-nodes-nospace-h: # buf < NODE_HEADER_SIZE ⊦ abs-nodes(buf, m, x, lax, boolvar) ↔ x = [] ∧ lax = [] ∧ buf = mkbuf(0);% ⊦ n + 0 = n; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (lax + lax0) + lax1 = lax + lax0 + lax1; from specification list[laddress-list]%a: ⊦ (x + y) + z = x + y + z; from specification list%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]% ⊦ m < n ↔ ¬ n ≤ m; (ss)