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Proof step 12 from proof abs-nodes-emptyheader-h (previous step)

abs-nodes(buf1, m + # buf0, [], [], weak), abs-padding(buf0), isempty(buf0 + buf1, 0, NODE_HEADER_SIZE) ⊦ buf0 + buf1 = mkbuf(0)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: abs-node name: abs-padding seq: ⊦ abs-padding(buf) ↔ (∃ buf0, buf1. buf = buf0 + buf1 + validtrailer ∧ is-encoded(nodeheader(# buf1, true), buf0) ∧ is-aligned(# buf1, 2 * NODE_HEADER_SIZE)) subst: [buf] → [buf0] flags: <all paths>

Additional information

Used simplifier rules: ⊦ #(buf + buf0) = # buf + # buf0; (s)% ⊦ # validtrailer = NODE_HEADER_SIZE; (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%lfw-is-encoded-nodeheader-size: ⊦ is-encoded(ndhd, buf) → # buf = NODE_HEADER_SIZE; (forward) from specification abs-node%m = # buf0 ⊦ isempty(buf0 + buf1, 0, m) ↔ isempty(buf0); (s)% ⊦ isempty(buf) ↔ buf = mkempbuf(# buf); (s)% ⊦ # mkempbuf(n) = n; (s)% ⊦ ¬ is-encoded(ndhd, mkempbuf(n)); (s) Used terms: buf0