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Proof step 22 from proof abs-nodes-no-padding-last (previous step)

# buf0 = (x0 + a ').flashsize, # buf1 = a0.alignedsize + 2 * NODE_HEADER_SIZE, abs-node(buf1, a0), abs-nodes(buf0, m0 + # buf1, x0 + a ', [], false), ∀ buf2, x, a, m, lax, ladr. # buf2 < #(buf1 + buf0) → # buf2 = (x + a ').flashsize ∧ abs-nodes(buf2, m, x + a ', lax + ladr ', false) → (∃ buf3, buf1. buf2 = buf3 + buf1 ∧ abs-nodes(buf3, m, x, lax, false) ∧ abs-node(buf1, a) ∧ ladr = @(# buf3 + m, 2 * NODE_HEADER_SIZE + a.alignedsize)) ⊦ ∃ buf3, buf2. buf1 + buf0 = buf3 + buf2 ∧ abs-nodes(buf3, m0, a0 ' + x0, [], false) ∧ abs-node(buf2, a) ∧ @(m0, # buf1) = @(# buf3 + m0, 2 * NODE_HEADER_SIZE + a.alignedsize)

User applied rule apply lemma

And obtained the following new goals

Rule argument

spec: <toplevel> name: abs-nodes-elems-adr-length-h seq: ⊦ abs-nodes(buf, m, x, lax, weak) → # x = # lax subst: [buf, m, x, lax, weak] → [buf0, m0 + # buf1, x0 + a ', [], false]

Additional information

Used simplifier rules: abs-nodes-unique-strong-h: ⊦ abs-nodes(buf, m, x0, lax0, false) → (abs-nodes(buf, m, x1, lax1, boolvar1) ↔ x0 = x1 ∧ lax0 = lax1);% ⊦ #(x + y) = # x + # y; (s)% ⊦ # a ' = 0 +1; (s)%a: ⊦ (x + y) + z = x + y + z; from specification list% ⊦ # [] = 0; (s)% ⊦ m + 1 ≠ 0; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic Used terms: buf0, m0 + # buf1, x0 + a ', [], false