Nuprl Lemma : perm_assoc
∀[T:Type]. ∀[p,q,r:Perm(T)]. (p O q O r = p O q O r ∈ Perm(T))
Proof
Definitions occuring in Statement :
comp_perm: comp_perm,
perm: Perm(T),
uall: ∀[x:A]. B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
member: t ∈ T,
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
perm: Perm(T),
prop: ℙ,
pi2: snd(t),
perm_b: p.b,
pi1: fst(t),
perm_f: p.f,
mk_perm: mk_perm(f;b),
comp_perm: comp_perm,
true: True,
squash: ↓T,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q
Lemmas referenced :
perm_wf,
comp_perm_wf,
perm_properties,
inv_funs_wf,
perm_f_wf,
perm_b_wf,
perm_sig_wf,
compose_wf,
mk_perm_wf,
equal_wf,
squash_wf,
true_wf,
comp_assoc,
subtype_rel_self,
iff_weakening_equal
Rules used in proof :
inhabitedIsType,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
hypothesisEquality,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesis,
because_Cache,
universeIsType,
universeEquality,
isect_memberFormation_alt,
sqequalRule,
isect_memberEquality,
isectElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
dependent_set_memberEquality,
setElimination,
rename,
natural_numberEquality,
applyEquality,
lambdaEquality,
imageElimination,
functionEquality,
imageMemberEquality,
baseClosed,
instantiate,
independent_isectElimination,
productElimination,
independent_functionElimination
Latex:
\mforall{}[T:Type]. \mforall{}[p,q,r:Perm(T)]. (p O q O r = p O q O r)
Date html generated:
2019_10_16-PM-00_58_56
Last ObjectModification:
2018_09_26-PM-08_11_06
Theory : perms_1
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