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Proof step 32 from proof abs-nodes-subarray-failed (previous step)

# buf0 = x0.flashsize, # buf1 = nd.alignedsize + 2 * NODE_HEADER_SIZE, abs-node(buf1, nd), abs-nodes(buf0, m0 + # buf1, x0, lax0, 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), lax0 = [], x0 = [], abs-nodes(buf1, m0, nd ', @(m0, # buf1) ', true)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 33:
⊦ abs-nodes(buf, m, a ', lax, weak) ↔ (∃ buf0, buf1. buf = buf0 + buf1 ∧ ( abs-padding(buf0) ∧ abs-nodes(buf1, m + # buf0, a ', lax, weak) ∨ lax = @(m, a.flashsize) ' ∧ abs-node(buf0, a) ∧ abs-nodes(buf1, m + # buf0, [], [], weak)))
Proof step 34:
# buf1 = nd.alignedsize + 2 * NODE_HEADER_SIZE, # buf0 = x0.flashsize, abs-node(buf1, nd), abs-nodes(buf0, m0 + # buf1, x0, lax0, 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), lax0 = [], x0 = [], ∃ buf0, buf2. buf1 = buf0 + buf2 ∧ ( abs-padding(buf0) ∧ abs-nodes(buf2, m0 + # buf0, nd ', @(m0, # buf1) ', true) ∨ @(m0, # buf1) ' = @(m0, nd.flashsize) ' ∧ abs-node(buf0, nd) ∧ abs-nodes(buf2, m0 + # buf0, [], [], true))

Rule argument

spec: <toplevel> name: abs-nodes-one-h seq: ⊦ abs-nodes(buf, m, a ', lax, weak) ↔ (∃ buf0, buf1. buf = buf0 + buf1 ∧ ( abs-padding(buf0) ∧ abs-nodes(buf1, m + # buf0, a ', lax, weak) ∨ lax = @(m, a.flashsize) ' ∧ abs-node(buf0, a) ∧ abs-nodes(buf1, m + # buf0, [], [], weak))) subst: [weak, lax, a, m, buf] → [true, @(m0, # buf1) ', nd, m0, buf1] flags: <all paths>

Additional information

Used terms: true, @(m0, # buf1) ', nd, m0, buf1