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Proof step 40 from proof abs-nodes-subarray-failed (previous step)

# buf1 = nd.alignedsize + 2 * NODE_HEADER_SIZE, # buf0 = (2 * NODE_HEADER_SIZE + a.alignedsize) + y.flashsize, abs-node(buf1, nd), abs-nodes(buf0, m0 + # buf1, a ' + y, [], false), ∀ buf2, x, n, m, lax. # buf2 < #(buf1 + buf0) → # buf2 = x.flashsize ∧ n < x.flashsize ∧ abs-nodes(buf2, m, x, lax, false) ∧ is-aligned(n, NODE_HEADER_SIZE) → n = 0 ∨ x = [] ∨ (∃ n0. n0 < # lax ∧ abs-nodes(subarray(buf2, 0, n), m, prefixn(n0, x), prefixn(n0, lax), true)) ⊦ buf1 + buf0 = mkbuf(0), buf1 = mkbuf(0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 41:
⊦ # buf = (a ' + x).flashsize → ( abs-nodes(buf, m, a ' + x, lax, false) ↔ (∃ buf0, buf1. buf = buf0 + buf1 ∧ lax ≠ [] ∧ lax.head.off = m ∧ lax.head.size = # buf0 ∧ abs-node(buf0, a) ∧ abs-nodes(buf1, m + # buf0, x, lax.tail, false)))

Rule argument

spec: <toplevel> name: abs-nodes-no-padding-rec seq: ⊦ # buf = (a ' + x).flashsize → ( abs-nodes(buf, m, a ' + x, lax, false) ↔ (∃ buf0, buf1. buf = buf0 + buf1 ∧ lax ≠ [] ∧ lax.head.off = m ∧ lax.head.size = # buf0 ∧ abs-node(buf0, a) ∧ abs-nodes(buf1, m + # buf0, x, lax.tail, false))) subst: [lax, x, a, m, buf] → [[], y, a, m0 + # buf1, buf0] flags: <all paths>

Additional information

Used simplifier rules: size-rec: ⊦ (a ' + x).flashsize = a.flashsize + x.flashsize;% ⊦ nd.flashsize = 2 * NODE_HEADER_SIZE + nd.alignedsize; (s)%a: ⊦ (x + y) + z = x + y + z; from specification list%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic Used terms: [], y, a, m0 + # buf1, buf0