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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