Nuprl Lemma : comp_perm_wf
∀T:Type. ∀p,q:Perm(T). (p O q ∈ Perm(T))
Proof
Definitions occuring in Statement :
comp_perm: comp_perm,
perm: Perm(T),
all: ∀x:A. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
comp_perm: comp_perm,
uall: ∀[x:A]. B[x],
perm: Perm(T),
implies: P ⇒ Q,
inv_funs: InvFuns(A;B;f;g),
and: P ∧ Q,
true: True,
squash: ↓T,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
prop: ℙ
Lemmas referenced :
mk_perm_wf_a,
compose_wf,
perm_f_wf,
perm_b_wf,
perm_wf,
perm_properties,
equal_wf,
istype-universe,
comp_id_l,
iff_weakening_equal,
squash_wf,
true_wf,
comp_assoc,
subtype_rel_self
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation_alt,
cut,
sqequalRule,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
isectElimination,
because_Cache,
setElimination,
rename,
hypothesis,
independent_functionElimination,
inhabitedIsType,
universeIsType,
universeEquality,
productElimination,
independent_pairFormation,
functionEquality,
natural_numberEquality,
equalityTransitivity,
equalitySymmetry,
applyEquality,
lambdaEquality_alt,
imageElimination,
functionIsType,
imageMemberEquality,
baseClosed,
independent_isectElimination,
instantiate,
promote_hyp
Latex:
\mforall{}T:Type. \mforall{}p,q:Perm(T). (p O q \mmember{} Perm(T))
Date html generated:
2019_10_16-PM-00_58_52
Last ObjectModification:
2018_10_08-AM-09_46_30
Theory : perms_1
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