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Proof step 47 from proof prepost-encode-group-nodes (previous step)

# gndx0 = # lax, # buf0 = gndx3.flashsize, # buf = 2 * NODE_HEADER_SIZE + gnd.alignedsize, # buf3 = gndx0.flashsize, # buf1 = # buf + gndx3.flashsize, subarray(buf1, # buf, gndx3.flashsize) = subarray(buf0 + buf, # buf, gndx3.flashsize), abs-node(subarray(buf1, 0, # buf), gnd), abs-nodes(buf3, n, gndx0, lax, false) ⊦ ∃ buf, buf0. buf3 + buf1 = buf + buf0 ∧ # buf = gndx0.flashsize + 2 * NODE_HEADER_SIZE + gnd.alignedsize ∧ abs-nodes(buf, n, gndx0 + gnd ', lax + @(n + gndx0.flashsize, 2 * NODE_HEADER_SIZE + gnd.alignedsize) ', false)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 48:
⊦ # buf = n0 + n1 ↔ (∃ buf0, buf1. buf = buf0 + buf1 ∧ # buf0 = n0 ∧ # buf1 = n1)
Proof step 49:
# buf3 = gndx0.flashsize, # buf = 2 * NODE_HEADER_SIZE + gnd.alignedsize, # buf0 = gndx3.flashsize, # gndx0 = # lax, subarray(buf1, # buf, gndx3.flashsize) = subarray(buf0 + buf, # buf, gndx3.flashsize), abs-node(subarray(buf1, 0, # buf), gnd), abs-nodes(buf3, n, gndx0, lax, false), ∃ buf0, buf2. buf1 = buf0 + buf2 ∧ # buf0 = # buf ∧ # buf2 = gndx3.flashsize ⊦ ∃ buf, buf0. buf3 + buf1 = buf + buf0 ∧ # buf = gndx0.flashsize + 2 * NODE_HEADER_SIZE + gnd.alignedsize ∧ abs-nodes(buf, n, gndx0 + gnd ', lax + @(n + gndx0.flashsize, 2 * NODE_HEADER_SIZE + gnd.alignedsize) ', false)

Rule argument

spec: array-splice, inst: buffer name: array-split-elim-size seq: ⊦ # buf = n0 + n1 ↔ (∃ buf0, buf1. buf = buf0 + buf1 ∧ # buf0 = n0 ∧ # buf1 = n1) subst: [n1, n0, buf] → [gndx3.flashsize, # buf, buf1] flags: <all paths>

Additional information

Used terms: gndx3.flashsize, # buf, buf1