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Proof step 9 from proof prepost-encode-group-nodes (previous step)

ax = [], buf = mkbuf(gndx.flashsize), err = ESUCCESS, m0 = 0, m1 = 0, m2 = n1, n = n0 ⊦ ⟪while err = ESUCCESS ∧ m1 < # gndx do {/* (prepost-encode-group-nodes : invariant m1 ≤ # gndx ∧ (err = ESUCCESS ∨ ⌊err⌋ ) ∧ ( err = ESUCCESS → # buf = # buf` ∧ (∃ gndx0, gndx1. gndx = gndx0 + gndx1 ∧ # gndx0 = m1 ∧ m0 = gndx0.flashsize ∧ (∃ lax, buf0, buf1. lax.to-adr(m2) = ax ∧ buf = buf0 + buf1 ∧ # buf0 = m0 ∧ abs-nodes(buf0, n, gndx0, lax, false)))) wfbound # gndx - m1) */; let m = ? in {encode_group_node#(gndx[m1], m0; m, buf; err); ax := ax + @(m2, n + m0, m); m0 := m0 + m}; m1 := m1 + 1}⟫ ((err = ESUCCESS ∨ ⌊err⌋ ) ∧ (err = ESUCCESS → (∃ lax. lax.to-adr(n1) = ax ∧ # buf = gndx.flashsize ∧ abs-nodes(buf, n0, gndx, lax, false))))

Heuristic annotation applied rule annotation right

And obtained the following new goals

Proof step 10:
ax0 = [], buf2 = mkbuf(gndx.flashsize), err = ESUCCESS, err0 = ESUCCESS, m1 = m, m2 = n1, m3 = 0, m4 = 0, n = n0, m1 < # gndx, m1 ≤ # gndx, err = ESUCCESS → # buf = # buf2 ∧ (∃ gndx0, gndx1. gndx = gndx0 + gndx1 ∧ # gndx0 = m1 ∧ m0 = gndx0.flashsize ∧ (∃ lax, buf0, buf1. lax.to-adr(m2) = ax ∧ buf = buf0 + buf1 ∧ # buf0 = m0 ∧ abs-nodes(buf0, n, gndx0, lax, false))), err = ESUCCESS ∨ ⌊err⌋ ⊦ ⟪let m = ? in {encode_group_node#(gndx[m1], m0; m, buf; err); ax := ax + @(m2, n + m0, m); m0 := m0 + m}; m1 := m1 + 1⟫ ( ( m1 ≤ # gndx ∧ (err = ESUCCESS ∨ ⌊err⌋ ) ∧ ( err = ESUCCESS → # buf = # buf2 ∧ (∃ gndx0, gndx1. gndx = gndx0 + gndx1 ∧ # gndx0 = m1 ∧ m0 = gndx0.flashsize ∧ (∃ lax, buf0, buf1. lax.to-adr(m2) = ax ∧ buf = buf0 + buf1 ∧ # buf0 = m0 ∧ abs-nodes(buf0, n, gndx0, lax, false))))) ∧ # gndx - m1 < # gndx - m)

Rule argument

rule: invariant right arg: bound: # gndx - m1 inv: m1 ≤ # gndx ∧ (err = ESUCCESS ∨ ⌊err⌋ ) ∧ ( err = ESUCCESS → # buf = # buf` ∧ (∃ gndx0, gndx1. gndx = gndx0 + gndx1 ∧ # gndx0 = m1 ∧ m0 = gndx0.flashsize ∧ (∃ lax, buf0, buf1. lax.to-adr(m2) = ax ∧ buf = buf0 + buf1 ∧ # buf0 = m0 ∧ abs-nodes(buf0, n, gndx0, lax, false)))) fmapos: right 1 pos: right 1

Additional information

Used simplifier rules: ⊦ # mkbuf(n) = n; (s)% ⊦ #(buf + buf0) = # buf + # buf0; (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]% ⊦ (gndx + gndx0).flashsize = gndx.flashsize + gndx0.flashsize; (s)%a: ⊦ (gndx + gndx0) + gndx1 = gndx + gndx0 + gndx1; from specification list[group-store]% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ m ≤ n → (n ≤ m ↔ m = n); (s)%abs-nodes-elems-adr-length-h: ⊦ abs-nodes(buf, m, gndx, lax, weak) → # gndx = # lax; (forward) from specification abs-list[encoding-group-node]% ⊦ #(gndx + gndx0) = # gndx + # gndx0; (s)% ⊦ m = m + n ↔ n = 0; (s)% ⊦ # gndx = 0 ↔ gndx = []; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ m + n = m + n0 ↔ n = n0; (s)% ⊦ m + n ≤ m + n0 ↔ n ≤ n0; (s)% ⊦ m ≤ m; (s)% ⊦ lax0.to-adr(n) = lax1.to-adr(n) ↔ lax0 = lax1; (s)% ⊦ [].flashsize = 0; (s)% ⊦ # buf = 0 ↔ buf = mkbuf(0); (s)% ⊦ gndx + [] = gndx; (s)%⊦ abs-nodes(buf0, m, gndx, lax0, false) → ( abs-nodes(buf0 + buf1, m, gndx, lax0, weak) ↔ abs-nodes(buf1, m + # buf0, [], [], weak)); (ss)% ⊦ abs-nodes(mkbuf(0), m, gndx, lax, weak) ↔ gndx = [] ∧ lax = []; (s)% ⊦ 0 ≤ m; (s)% ⊦ lax.to-adr(n) = [] ↔ lax = []; (s)% ⊦ # buf = 0 → buf + buf0 = buf0; (s)% ⊦ [] + gndx = gndx; (s) Used formulas: m1 ≤ # gndx ∧ (err = ESUCCESS ∨ ⌊err⌋ ) ∧ ( err = ESUCCESS → # buf = # buf` ∧ (∃ gndx0, gndx1. gndx = gndx0 + gndx1 ∧ # gndx0 = m1 ∧ m0 = gndx0.flashsize ∧ (∃ lax, buf0, buf1. lax.to-adr(m2) = ax ∧ buf = buf0 + buf1 ∧ # buf0 = m0 ∧ abs-nodes(buf0, n, gndx0, lax, false)))), # gndx - m1 = # gndx - m1