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Proof step 27 from proof abs-nodes-one-abs-node (previous step)

# buf1 = NODE_HEADER_SIZE, # buf0 = a.alignedsize, is-encoded(a, subarray(buf0, 0, node-size-headerless(a))), is-encoded(nodeheader(node-size-headerless(a), false), buf1) ⊦ ∃ buf, buf2. buf1 + buf0 + validtrailer = buf + buf2 ∧ ( abs-padding(buf) ∧ abs-nodes(buf2, m + # buf, a ', @(m, 2 * NODE_HEADER_SIZE + a.alignedsize) ', false) ∨ 2 * NODE_HEADER_SIZE + a.alignedsize = # buf ∧ abs-node(buf, a) ∧ abs-nodes(buf2, m + # buf, [], [], false))

User applied rule exists right

And closed the goal!

Rule argument

pos: right 1 terms: buf1 + buf0 + validtrailer, mkbuf(0) abort: F discard: T computed: F

Additional information

Used simplifier rules: abs-nodes-mkbuf0-empty-h: ⊦ abs-nodes(mkbuf(0), m, x, lax, weak) ↔ x = [] ∧ lax = [];% ⊦ buf + mkbuf(0) = buf; (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]% ⊦ buf + buf0 = buf + buf1 ↔ buf0 = buf1; (s)% ⊦ #(buf + buf0) = # buf + # buf0; (s)% ⊦ # validtrailer = NODE_HEADER_SIZE; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ a ' ≠ []; (s)%m2 ≠ 0 ⊦ (* m2) * m + n = m + n0 ↔ (m2 - 1) * m + n = n0; (s)% ⊦ m0 * 1 = m0; (s)%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult%mult-c: ⊦ m * n = n * m; from specification nat-mult%c: ⊦ m + n = n + m; from specification nat-basic%⊦ # buf1 = nd.alignedsize ∧ is-encoded(nodeheader(node-size-headerless(nd), false), buf0) ∧ is-encoded(nd, subarray(buf1, 0, node-size-headerless(nd))) → abs-node(buf0 + buf1 + validtrailer, nd); (ss) Used terms: buf1 + buf0 + validtrailer, mkbuf(0)