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Proof step 2 from proof btree-clean-fwd (previous step)

((btree(rp0, r0, adr, height0, false, ri0, iast, as0, alladrs0, nstat) * P0))(zh0), ((btree(rp1, r1, adr, height1, false, ri1, iast, as1, alladrs1, nstat) * P1))(zh1) ⊦ height0 = height1 ∧ as0 = as1 ∧ ri0 = ri1 ∧ alladrs0 = alladrs1

User applied rule structural induction

And obtained the following new goals

Proof step 3:
((btree(rp1, r1, adr, height1, false, ri1, iast, as1, alladrs1, nstat) * P1))(zh1), ((btree(rp0, r0, adr, 0, false, ri0, iast, as0, alladrs0, nstat) * P0))(zh0) ⊦ 0 = height1 ∧ as0 = as1 ∧ ri0 = ri1 ∧ alladrs0 = alladrs1
Proof step 9:
((btree(rp1, r1, adr, height1, false, ri1, iast, as1, alladrs1, nstat) * P1))(zh1), ((btree(rp0, r0, adr, height +1, false, ri0, iast, as0, alladrs0, nstat) * P0))(zh0), ∀ rp0, r0, adr, ri0, iast, as0, alladrs0, nstat, P0, zh0, rp1, r1, height1, ri1, as1, alladrs1, P1, zh1. ((btree(rp0, r0, adr, height, false, ri0, iast, as0, alladrs0, nstat) * P0))(zh0) ∧ ((btree(rp1, r1, adr, height1, false, ri1, iast, as1, alladrs1, nstat) * P1))(zh1) → height = height1 ∧ as0 = as1 ∧ ri0 = ri1 ∧ alladrs0 = alladrs1 ⊦ height +1 = height1 ∧ as0 = as1 ∧ ri0 = ri1 ∧ alladrs0 = alladrs1

Rule argument

indvar: height0

Additional information

Used simplifier rules: nat freely generated by 0, +1;;