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Proof step 17 from proof abs-nodes-split-h (previous step)

@(m0, m1) ' + lax0 = lax1 + lax, abs-nodes(buf2 + buf, m + # buf1, nd ' + x + x1, lax1 + lax, weak), abs-nodes(buf, (m + # buf1) + # buf2, x1, lax, weak), abs-nodes(buf2, m + # buf1, nd ' + x, lax1, false), abs-padding(buf1), @(m0, m1) ∈ lax1 ∨ @(m0, m1) ∈ lax, ∀ buf3, m, x0, x1, lax, weak. # buf3 < #(buf1 + buf2 + buf) → abs-nodes(buf3, m, x0 + x1, lax, weak) → (∃ buf4, buf1, lax0, lax1. lax = lax0 + lax1 ∧ buf3 = buf4 + buf1 ∧ abs-nodes(buf4, m, x0, lax0, false) ∧ abs-nodes(buf1, m + # buf4, x1, lax1, weak)) ⊦ ∃ buf3, buf4, lax2, lax1. @(m0, m1) ' + lax0 = lax2 + lax1 ∧ buf1 + buf2 + buf = buf3 + buf4 ∧ abs-nodes(buf3, m, nd ' + x, lax2, false) ∧ abs-nodes(buf4, m + # buf3, x1, lax1, weak)

User applied rule exists right

And closed the goal!

Rule argument

pos: right 1 terms: buf1 + buf2, buf, lax1, lax abort: F discard: T computed: T

Additional information

Used simplifier rules: abs-nodes-padding-prefix: ⊦ abs-padding(buf0) → ( abs-nodes(buf0 + buf1, m, x, lax, weak) ↔ abs-nodes(buf1, m + # buf0, x, lax, weak));%abs-nodes-unique-strong-h: ⊦ abs-nodes(buf, m, x0, lax0, false) → (abs-nodes(buf, m, x1, lax1, boolvar1) ↔ x0 = x1 ∧ lax0 = lax1);%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%c: ⊦ m + n = n + m; from specification nat-basic Used terms: buf1 + buf2, buf, lax1, lax