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Proof step 38 from proof abs-nodes-unique-weak-h (previous step)

lax0.head = @(m0, m1), abs-nodes(buf0, m + # buf1, nd ' + x, lax0, true), abs-padding(buf1), # buf1 + # buf0 = 0 ∨ buf1 + buf0 = buf + buf2 ∧ abs-padding(buf) ∧ abs-nodes(buf2, m + # buf, [], [], true) ∨ abs-failed(buf1 + buf0), ∀ buf2, m, x0, lax0, x1, lax1. # buf2 < #(buf1 + buf0) → abs-nodes(buf2, m, x0, lax0, true) ∧ abs-nodes(buf2, m, x1, lax1, true) → x0 = x1 ∧ lax0 = lax1 ⊦

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 39:
abs-nodes(buf0, m + # buf1, nd ' + x, @(m0, m1) ' + lax, true), abs-padding(buf1), # buf1 + # buf0 = 0 ∨ buf0 = buf2 ∧ buf1 = buf ∧ abs-nodes(buf2, m + # buf, [], [], true), ∀ buf2, m, x0, lax0, x1, lax1. # buf2 < #(buf1 + buf0) → abs-nodes(buf2, m, x0, lax0, true) ∧ abs-nodes(buf2, m, x1, lax1, true) → x0 = x1 ∧ lax0 = lax1 ⊦

Rule argument

Additional information

Used simplifier rules: abs-nodes-first-adr-explicit: ⊦ abs-nodes(buf, m, a ' + x, lax, weak) → (lax.head = ladr ↔ (∃ lax0. lax = ladr + lax0));% ⊦ ladr ∈ ladr0 ' + lax ↔ ladr = ladr0 ∨ ladr ∈ lax; (s)%a: ⊦ (lax + lax0) + lax1 = lax + lax0 + lax1; from specification list[laddress-list]%in-14: ⊦ ladr ' + lax = lax0 → ladr ∈ lax0; (forward) from specification list[laddress-list]% ⊦ abs-padding(buf0) → ¬ abs-failed(buf0 + buf1); (s)% ⊦ buf + buf0 = buf + buf1 ↔ buf0 = buf1; (s)%⊦ buf0 + buf1 = buf2 + buf3 ∧ abs-padding(buf0) → (abs-padding(buf2) ↔ buf0 = buf2); (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]% ⊦ ladr + lax = ladr ' + lax; (s)%a: ⊦ (x + y) + z = x + y + z; from specification list