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Proof step 44 from proof abs-nodes-unique-weak-h (previous step)

lax0.head = @(m0, m1), abs-nodes(buf1 + buf0, m, nd0 ' + x2, lax1, true), abs-nodes(buf0, m + # buf1, nd ' + x, lax0, true), abs-padding(buf1), ∀ 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 ⊦ nd ' + x = nd0 ' + x2 ∧ lax0 = lax1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 45:
abs-nodes(buf0, m + # buf1, nd0 ' + x2, lax1, true), abs-nodes(buf0, m + # buf1, nd ' + x, @(m0, m1) ' + lax, true), abs-padding(buf1), ∀ 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 ⊦ nd ' + x = nd0 ' + x2 ∧ @(m0, m1) ' + lax = 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));%abs-nodes-padding-prefix: ⊦ abs-padding(buf0) → ( abs-nodes(buf0 + buf1, m, x, lax, weak) ↔ abs-nodes(buf1, m + # buf0, x, lax, weak));% ⊦ 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]%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