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Theorem maxpath-array

⊦ is_array(str, r, st) ∧ st[r -- i '] = refval(r0) ∧ 0 ≤ i ∧ i < st[r -- _length] .intval ∧ ¬ junkref(str, r, st) ∧ ¬ cyclic(str, r, st) → ¬ maxpath(str, r, st) ≤ maxpath(str, r0, st)

Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by: cyclic-pseq, maxpath-array-ls, pseq-subset, pseq-sym-01,
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 23
Proof steps: 50
Used lemmas: maxpath-max, validrefset-empty, validrefset-def, maxpath-in, maxpath-zero,
Used spec theorems:
Used simplifier rules:
- set-basic/reflistset/In-empty
- nat/lez
- cyclic/validrefs-null-02
- addfuns/is_valid_ref-null
- javavalue/sel-09
- javavalue/test-19
- int-abs/lels-03
- int-abs/lels-04
- int-abs/lels
- int-abs/lels-01
- typefuns/ref
- list/references/in-06
- list-dup/references/c-02
- list/references/in-17
- list/references/in-append
- list-dup/references/rec
- list-last/references/l-05
- list/references/c-08
- list/references/e
- list/references/app-02-ant
- cyclic/validrefs-not
- nat/le-num-02
- nat/le-add
- nat/let
- nat/lels
- nat-basic2/s
- list-data/references/l
- nat-basic1/lf-01
- nat/lez-01
- nat-basic1/less-1
- nat-basic1/f
- nat/eqle-one
- list-dup/references/dups-cons
- nat-basic2/c
- nat-basic2/a
- nat/succ-01
- list/references/e-01
- list/references/a
- list/references/len-02
- list/references/len
- list/references/c
- list-data/references/elim-list-c
- addfuns/is_valid_ref-isarray
- set-basic/reflistset/size-zero
- set-basic/reflistset/size-zero-01
- int-abs/forward-le-01
- int-abs/forward-le-05