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Proof step 15 from proof abs-nodes-padding-prefix (previous step)

abs-padding(buf0) ⊦ (∃ buf, buf2. buf0 + buf1 = buf + buf2 ∧ ( buf0 = buf ∧ abs-nodes(buf2, m + # buf, nd ' + x0, @(m0, m1) ' + lax0, weak) ∨ m0 = m ∧ m1 = # buf ∧ abs-node(buf, nd) ∧ abs-nodes(buf2, m + # buf, x0, lax0, weak))) ↔ abs-nodes(buf1, m + # buf0, nd ' + x0, @(m0, m1) ' + lax0, weak)

User applied rule case distinction

And obtained the following new goals

Proof step 16:
abs-padding(buf0), ∃ buf, buf2. buf0 + buf1 = buf + buf2 ∧ ( buf0 = buf ∧ abs-nodes(buf2, m + # buf, nd ' + x0, @(m0, m1) ' + lax0, weak) ∨ m0 = m ∧ m1 = # buf ∧ abs-node(buf, nd) ∧ abs-nodes(buf2, m + # buf, x0, lax0, weak)) ⊦ abs-nodes(buf1, m + # buf0, nd ' + x0, @(m0, m1) ' + lax0, weak)
Proof step 18:
abs-nodes(buf1, m + # buf0, nd ' + x0, @(m0, m1) ' + lax0, weak), abs-padding(buf0) ⊦ ∃ buf, buf2. buf0 + buf1 = buf + buf2 ∧ ( buf0 = buf ∧ abs-nodes(buf2, m + # buf, nd ' + x0, @(m0, m1) ' + lax0, weak) ∨ m0 = m ∧ m1 = # buf ∧ abs-node(buf, nd) ∧ abs-nodes(buf2, m + # buf, x0, lax0, weak))

Rule argument

pos: right 1

Proof step 15 from proof abs-nodes-padding-prefix (previous step)

User applied rule case distinction

And obtained the following new goals

Rule argument

Additional information