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Theorem gcd-loop-partial
inv(n, m, N, M) ⊦ [: N, M | rely(N', M', N'', M''), rely(M, N, M', N'), inv(n, m, N, M), GCD_loop(; N, M)] (N = M ∧ N = gcd(n, m))
Type: A user defined theorem
Validity: The proof is valid.
Features: tl,
Comment:
Used by:
gcd-partial
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 5
Proof steps: 32
Used lemmas:
inv
,
rely
,
Used spec theorems:
Used simplifier rules:
nat-basic1
/
ref-1
nat-prime
/
gcd-id
nat
/
ler
nat
/
anti
nat-basic1
/
trans-1
nat-basic1
/
lf
nat-basic1
/
lf-01
nat-prime
/
gcd-add
nat-prime
/
gcd-sym
nat-mult
/
two-02
nat
/
ls-02
nat
/
ls-03
nat
/
elim-sub
nat-mult
/
mult-c
nat-mult
/
mult-a
nat-mult
/
one
nat-mult
/
numeral-26
nat
/
lep
nat-basic2
/
l-01
nat-basic2
/
eq
nat-basic2
/
succ
nat
/
lels
nat
/
le-add
nat
/
lels-01
nat-basic1
/
ls-02
nat
/
lels-02
nat
/
fle-01
nat-basic1
/
neq-01
nat-basic2
/
c
nat-basic2
/
a
nat-basic1
/
f
nat-basic1
/
lf-02
nat
/
fle
nat
/
let