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Proof step 7 from proof abs-padding-eq (previous step)

# buf = NODE_HEADER_SIZE, # buf5 = NODE_HEADER_SIZE, buf5 + (buf6 + validtrailer) + buf1 = buf + (buf4 + validtrailer) + buf3, is-aligned(# buf6, 2 * NODE_HEADER_SIZE), is-aligned(# buf4, 2 * NODE_HEADER_SIZE), is-encoded(nodeheader(# buf6, true), buf5), is-encoded(nodeheader(# buf4, true), buf) ⊦ buf5 + buf6 = buf + buf4

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: array-splice, inst: buffer name: append-inj seq: ⊦ # buf = # buf0 → (buf + buf1 = buf0 + buf2 ↔ buf = buf0 ∧ buf1 = buf2) subst: [buf2, buf0, buf1, buf] → [(buf4 + validtrailer) + buf3, buf, (buf6 + validtrailer) + buf1, buf5] flags: <all paths>

Additional information

Used simplifier rules: ⊦ buf + buf0 = buf + buf1 ↔ buf0 = buf1; (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]% ⊦ is-encoded(ndhd, buf) → (is-encoded(ndhd0, buf) ↔ ndhd = ndhd0); (s)%⊦ nodeheader(m, boolvar) = nodeheader(m0, boolvar0) ↔ m = m0 ∧ (boolvar ↔ boolvar0); (ws)%⊦ # buf = # buf0 → (buf + buf1 = buf0 + buf2 ↔ buf = buf0 ∧ buf1 = buf2); (ws) Used terms: (buf4 + validtrailer) + buf3, buf, (buf6 + validtrailer) + buf1, buf5