Nuprl Lemma : app_perm_wf
∀m,n:ℕ. ∀p:Sym(m). ∀q:Sym(n). (app_perm(m;n;p;q) ∈ Sym(m + n))
Proof
Definitions occuring in Statement :
app_perm: app_perm(m;n;p;q)
,
sym_grp: Sym(n)
,
nat: ℕ
,
all: ∀x:A. B[x]
,
member: t ∈ T
,
add: n + m
Definitions unfolded in proof :
all: ∀x:A. B[x]
,
member: t ∈ T
,
app_perm: app_perm(m;n;p;q)
,
uall: ∀[x:A]. B[x]
,
nat: ℕ
,
sym_grp: Sym(n)
,
perm: Perm(T)
,
implies: P
⇒ Q
,
inv_funs: InvFuns(A;B;f;g)
,
and: P ∧ Q
,
true: True
,
squash: ↓T
,
prop: ℙ
,
subtype_rel: A ⊆r B
,
uimplies: b supposing a
,
guard: {T}
,
iff: P
⇐⇒ Q
,
rev_implies: P
⇐ Q
Lemmas referenced :
mk_perm_wf_a,
int_seg_wf,
app_permf_wf,
perm_f_wf,
perm_b_wf,
perm_wf,
nat_wf,
perm_properties,
tidentity_wf,
equal_wf,
squash_wf,
true_wf,
istype-universe,
app_permf_comp,
subtype_rel_self,
app_permf_id,
iff_weakening_equal
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation_alt,
cut,
sqequalRule,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
isectElimination,
natural_numberEquality,
addEquality,
setElimination,
rename,
because_Cache,
hypothesis,
hypothesisEquality,
independent_functionElimination,
universeIsType,
inhabitedIsType,
productElimination,
independent_pairFormation,
functionEquality,
applyEquality,
lambdaEquality_alt,
imageElimination,
equalityTransitivity,
equalitySymmetry,
universeEquality,
imageMemberEquality,
baseClosed,
instantiate,
functionIsType,
independent_isectElimination
Latex:
\mforall{}m,n:\mBbbN{}. \mforall{}p:Sym(m). \mforall{}q:Sym(n). (app\_perm(m;n;p;q) \mmember{} Sym(m + n))
Date html generated:
2019_10_16-PM-00_59_44
Last ObjectModification:
2018_10_08-AM-09_20_27
Theory : perms_1
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