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Proof step 17 from proof abs-nodes-inv-flashsize-h (previous step)

# gndx0 = # lax0, abs-node(buf1, gnd), abs-nodes(buf0, m + # buf1, gndx0, lax0, weak), ∀ buf2, m, gndx, lax, weak. # buf2 < #(buf1 + buf0) → abs-nodes(buf2, m, gndx, lax, weak) → inv-flashsize(gndx, lax) ⊦ 2 * NODE_HEADER_SIZE + gnd.alignedsize = # buf1 ∧ inv-flashsize(gndx0, lax0)

User applied rule apply induction

And obtained the following new goals

Proof step 18:
# gndx0 = # lax0, abs-node(buf1, gnd), abs-nodes(buf0, m + # buf1, gndx0, lax0, weak), inv-flashsize(gndx0, lax0), ∀ buf2, m, gndx, lax, weak. # buf2 < #(buf1 + buf0) → abs-nodes(buf2, m, gndx, lax, weak) → inv-flashsize(gndx, lax) ⊦ 2 * NODE_HEADER_SIZE + gnd.alignedsize = # buf1 ∧ inv-flashsize(gndx0, lax0)

Rule argument

subst: [buf2, m, gndx, lax, weak] → [buf0, m + # buf1, gndx0, lax0, weak]

Additional information

Used simplifier rules: ⊦ #(buf + buf0) = # buf + # buf0; (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ m + m0 ≤ m ↔ m0 = 0; (s)% ⊦ # buf = 0 ↔ buf = mkbuf(0); (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ ¬ abs-node(mkbuf(0), gnd); (s) Used terms: buf0, m + # buf1, gndx0, lax0, weak